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no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 10px 0px;font-size:16px;font-weight:700;} @media (min-width:768px){.gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption 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no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 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href="//www.newsama.com/journals/am/" aria-label="Advances in Multimedia">多媒体的发展</一个>/<一个class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/am/contents/year/2011/" aria-label="2011">2011年</一个>/<年代p一个nclass="sc-bhlBdH UVThf">文章</年代p一个n></d我v><d我vclass="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 dDyxFF threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-eKZiaR dzZrgS section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</button> <div class="sc-bEjcJn jLUVhb static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-cbkKFq prcY sc-bGbJRg dVCLgr left_section_menu"> <p>在这一页上</p><年代p一个nclass="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#abstract" aria-label="">文摘</一个></年代p一个n><年代pan class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#introduction" aria-label="">介绍</一个></年代p一个n><年代pan class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#conclusion" aria-label="">结论</一个></年代p一个n><年代pan class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#references" aria-label="">引用</一个></年代p一个n><年代pan class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#copyright" aria-label="">版权</一个></年代p一个n></d我v> </div> </div> <div class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-chbbiW mBGSe article_header_class"> <p class="sc-kZmsYB bkiEfx article_type">研究文章|开放获取</p><d我vclass="sc-RcBXQ ztvYg article_citation"> 体积 2011年 <span class="sc-fZwumE cUsFHx">|</年代p一个n>文章的ID 421820年 <span class="sc-fZwumE cUsFHx">|</年代p一个n><一个class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2011/421820" aria-label="Doi-link">https://doi.org/10.1155/2011/421820</一个></d我v><d我vclass="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>对此Shishibori大地小泉,吴克群北城, ”<年代p一个nclass="adjust-article-svg-size">快速检索算法挖土机的距离使用EMD下界和跳过算法</年代p一个n>”,<i>多媒体的发展</我>, 卷。2011年, 文章的ID421820年, 9   页面, 2011年。 https://doi.org/10.1155/2011/421820</p></d我v><button class="sc-hSdWYo etauus sc-iBEsjs kPshFw" color="">显示引用</button> </div> <h1 class="sc-iRbamj jZOxOO sc-iSDuPN kEVvRd article_title adjust-article-svg-size heading-title">快速检索算法挖土机的距离使用EMD下界和跳过算法</h1> </div> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class=""><b>对此Shishibori</b><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-hjRWVT irNWJI icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a>,<年代up>1</年代up></年代p一个n><年代pan class="">大地小泉,<年代up>1</年代up>和</年代p一个n><年代p一个nclass="">吴克群北城<一个class="sc-htpNat bUhGXt link" href="http://orcid.org/0000-0003-3275-3667" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-iybRtq iQSObO" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a><sup>2</年代up></年代p一个n><d我v class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</年代up><年代p一个n>部门的信息解决方案,技术和科学研究所,德岛大学的2 - 1 Minami-Josanjima-Cho, Tokushima-Shi, 770 - 8506年德岛,日本</年代p一个n></p><p><sup>2</年代up><年代p一个n>德岛大学的先进信息技术中心,2 - 1 Minami-Josanjima-Cho, Tokushima-Shi, 770 - 8506年德岛,日本</年代p一个n></p></d我v> <button class="sc-hSdWYo etauus sc-iQtOjA kfDwZY" color="">显示更多</button> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</b>位于拉詹</d我v><d我vclass="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">02年9月2010年</年代p一个n></d我v><d我vclass="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">修改后的</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年1月20日</年代p一个n></d我v><d我vclass="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年3月19日</年代p一个n></d我v><d我vclass="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年5月17日</年代p一个n></d我v></d我v> </div> <article class="sc-jtRlXQ gvEcCq article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4> <p>挖土机的距离(EMD)是衡量两个分布之间的距离,它已广泛应用于多媒体信息检索系统中,尤其是在基于内容的图像检索系统。EMD时基于颜色或纹理图像问题,EMD反映了人类知觉相似性。然而,它的使用在大型数据库中计算太贵了。为了实现有效的计算EMD在查询处理中,我们已经开发出“fastEMD,”库高速在大型数据库中基于特征相似性检索。介绍了技术用于fastEMD的实现和执行广泛的实验来证明它的效率。</p><年代p一个nclass="end-abs"></span> <h4 id="introduction">1。介绍</h4> <p>挖土机的距离(EMD)中引入计算机视觉作为改善两个分布之间的距离度量,它已广泛应用于多媒体数据库。特别是,在基于内容的图像检索(CBIR)的面积,在彩色图像从多媒体检索数据库,应用改进的距离是很重要的措施。几个CBIR模型提出了基于直方图的方法,如按图像内容(QBIC)方法提出的查询法等。<一个href="#B1">1</一个>),每个图像映射到一个向量基于编码的属性,如颜色分布,纹理和形状。然而,直方图的方法使用欧氏距离和二次形式应用向垃圾箱距离函数;因此,这些方法对小特征值分布的变化很敏感。</p><p>E米D的相似性距离计算的数量变化需要变换到另一个图像特征。Rubner和预<一个href="#B2">2</一个>使用EMD)提出了CBIR模型,和它的高质量的图像相似度搜索已经证明。Shishibori et al。<一个href="#B3">3</一个>使用EMD)提出了一个音乐检索模型,和query-by-humming系统提出了一种更健壮的方法比传统的方法。</p><p>E米D被定义为一个线性规划问题,可以使用单纯形法解决。然而,计算使用EMD和单纯形法太复杂的应用程序在交互多媒体数据库系统。为了实现高效检索处理大型多媒体数据库基于EMD,我们提出一个快速检索EMD算法。</p><p>为了减少计算时间的距离,该方法使用较低的边界距离科恩和Guibas中描述<一个href="#B4">4</一个>和同意等。<一个href="#B5">5</一个>]。的下边界距离EMD是一个简单的近似计算。在的情况下<年代vg height="10.7375" id="M1" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>最近邻搜索任务,这种方法计算原始EMD第一<年代vg height="10.7375" id="M2" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像,最大距离设置为阈值。这种方法计算边界距离越低<年代vg height="11.325" id="M3" style="vertical-align:-0.51414pt;width:34.0625px;" version="1.1" viewbox="0 0 34.0625 11.325" width="34.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5522919" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.892513" y="0"> 1</t年代p一个n></text> </g> </g> </svg>图像。这种方法不计算原始EMD如果边界距离超过阈值越低,因为真正的EMD不能低于第一<年代vg height="10.7375" id="M4" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像。在所有其他情况下,该方法计算原始EMD,如果真正的EMD低于第一<年代vg height="10.7375" id="M5" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图片,注册一个新的映像和阈值重置。</p><p>本文余下部分组织如下:部分<一个href="#sec2">2</一个>介绍了轮廓挖土机的距离。部分<一个href="#sec3">3</一个>解释了EMD的下界,提出计算的算法使用下界跳过。部分<一个href="#sec4">4</一个>评估方法的有效性通过实验结果。部分<一个href="#sec5">5</一个>描述了结论和未来的工作。</p><h4 id="earth-mover’s-distance">2。挖土机的距离</h4> <h5 id="sec2.1">2.1。传统的不同措施</h5> <p>的<年代vg height="16.237499" id="M6" style="vertical-align:-4.74141pt;width:17.1625px;" version="1.1" viewbox="0 0 17.1625 16.237499" width="17.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2375)"> <g transform="translate(72,-59.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>距离是一个广义的两个直方图之间的相似性<年代vg height="14.775" id="M7" style="vertical-align:-3.2316pt;width:55.737499px;" version="1.1" viewbox="0 0 55.737499 14.775" width="55.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.381809" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.68,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.46,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.775" id="M8" style="vertical-align:-3.2316pt;width:54.049999px;" version="1.1" viewbox="0 0 54.049999 14.775" width="54.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.706648" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.03,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.81,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代p一个n></text> </g> </g> </svg>。的<年代vg height="16.237499" id="M9" style="vertical-align:-4.74141pt;width:17.1625px;" version="1.1" viewbox="0 0 17.1625 16.237499" width="17.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2375)"> <g transform="translate(72,-59.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>距离的定义是<年代p一个nclass="equation" id="EEq1"> <svg height="51.762501" id="M10" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 51.762501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,51.7625)"> <g transform="translate(72,-30.59)"> <text transform="matrix(1,0,0,-1,132.21,46.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,141.06,43.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,147.92,46.97)"> <tspan style="font-size: 12.50px; " x="42.130001" y="9.7399998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.253901" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.455387" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.082218" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,206.05,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.15,40.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.68,33.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,216.31,48.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="1.58"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.68,43.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,231.68,46.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.23,43.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,252.45,48.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.95,53.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.73,37.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,269.83,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8090558" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,281.42,46.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="192.7" y="-1.2"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="196.86349" y="-1.2"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="203.11501" y="-1.2"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="13.55" id="M11" style="vertical-align:-2.29482pt;width:34.974998px;" version="1.1" viewbox="0 0 34.974998 13.55" width="34.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5772982" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.617687" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。</p><p>闵可夫斯基距离的值取决于假定不同的名称<年代vg height="9.875" id="M12" style="vertical-align:-2.29482pt;width:7.7624998px;" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。如果<年代vg height="13.55" id="M13" style="vertical-align:-2.29482pt;width:34.974998px;" version="1.1" viewbox="0 0 34.974998 13.55" width="34.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5772982" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.617687" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,被称为曼哈顿距离的距离。欧氏距离计算(<一个href="#EEq1">1</一个>)通过选择<年代vg height="13.55" id="M14" style="vertical-align:-2.29482pt;width:34.974998px;" version="1.1" viewbox="0 0 34.974998 13.55" width="34.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5772982" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.617687" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。欧几里得距离距离是最简单、最受欢迎的措施。</p><p>的<年代vg height="16.237499" id="M15" style="vertical-align:-4.74141pt;width:17.1625px;" version="1.1" viewbox="0 0 17.1625 16.237499" width="17.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2375)"> <g transform="translate(72,-59.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>距离是一个代表bin-by-bin不同措施,它被用作不同的多媒体信息检索系统的措施。这种方法的主要缺点是,它仅占之间的对应关系垃圾箱用相同的指数,在垃圾箱和它不使用信息。这是见图<一个href="//www.newsama.com/journals/am/2011/421820/fig1/" target="_blank">1</一个>,它显示了两对一维灰度直方图中描述Rubner和预<一个href="#B2">2</一个>]。</p><d我vclass="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="(一)Lp的距离。”n一个米e=”421820。fig.001a" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.001a.jpg"> <br> <strong>(一)Lp的距离。</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b)感知不同。”n一个米e=”421820。fig.001b" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.001b.jpg"> <br> <strong>(b)感知不同。</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig1"> <button class="partial-carousel-dot" aria-label="(a) Lp distance."><img alt="(一)Lp的距离。”n一个米e=”421820。fig.001a" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.001a.jpg"><br><strong>(一)Lp的距离。</年代trong></button> <button class="partial-carousel-dot" aria-label="(b) Perceptual dissimilarity."><img alt="(b)感知不同。”n一个米e=”421820。fig.001b" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.001b.jpg"><br><strong>(b)感知不同。</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig1"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 感知不同的插图。</t一个ble> </div> </div> </div> <p>虽然两直方图左边是相同的除了一本转变,<年代vg height="14.2375" id="M16" style="vertical-align:-3.13504pt;width:17.2875px;" version="1.1" viewbox="0 0 17.2875 14.2375" width="17.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>他们之间的距离大于<年代vg height="14.2375" id="M17" style="vertical-align:-3.13504pt;width:17.2875px;" version="1.1" viewbox="0 0 17.2875 14.2375" width="17.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>右边的两个直方图之间的距离。如图<一个href="//www.newsama.com/journals/am/2011/421820/fig1/" target="_blank">1(一)</一个>,<年代vg height="16.237499" id="M18" style="vertical-align:-4.74141pt;width:17.1625px;" version="1.1" viewbox="0 0 17.1625 16.237499" width="17.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2375)"> <g transform="translate(72,-59.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>距离不匹配感知不同。这可以固定使用箱子两个直方图之间的通讯和地面之间的距离,如图<一个href="//www.newsama.com/journals/am/2011/421820/fig1/" target="_blank">1 (b)</一个>。如图<一个href="//www.newsama.com/journals/am/2011/421820/fig1/" target="_blank">1 (b)</一个>,感知不同之间的通信是基于两个直方图的垃圾箱。</p><p>二次形式的距离是一个代表cross-bin不同措施。Niblack et al。<一个href="#B6">6</一个>)建议使用这个距离基于颜色的检索。二次形式的距离不执行质量元素之间的一一对应两个直方图。相同的质量在一个给定的本的直方图是由对应于群众中包含不同的垃圾箱的直方图。但是,使用二次形式的距离图像复现结果包括一些假阳性,因为二次形式的距离往往高估共同相似的颜色分布,前锋和Orengo所<一个href="#B7">7</一个>]。</p><h5 id="sec2.2">2.2。挖土机的距离</h5> <p>EMD是基于下列线性规划问题。让<年代vg height="17.4625" id="M19" style="vertical-align:-5.37971pt;width:190.75px;" version="1.1" viewbox="0 0 190.75 17.4625" width="190.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.4625)"> <g transform="translate(72,-58.03)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.930502" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.931942" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.09544" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.73,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.86,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-12.96,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-8.68,58.13)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-4.56,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.364747" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.955748" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.332996" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.496498" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,39.06,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,45.77,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,60.67,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,64.95,58.13)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,70.38,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> }</t年代p一个n></text> </g> </g> </svg>是第一个签名的<年代vg height="7.1374998" id="M20" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>集群,<年代vg height="11.05" id="M21" style="vertical-align:-3.2316pt;width:11.7875px;" version="1.1" viewbox="0 0 11.7875 11.05" width="11.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>集群代表和吗<年代vg height="14.0375" id="M22" style="vertical-align:-5.39853pt;width:21.262501px;" version="1.1" viewbox="0 0 21.262501 14.0375" width="21.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0375)"> <g transform="translate(72,-60.77)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.98,60.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>集群的重量。让<年代vg height="17.4625" id="M23" style="vertical-align:-5.37971pt;width:182.825px;" version="1.1" viewbox="0 0 182.825 17.4625" width="182.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.4625)"> <g transform="translate(72,-58.03)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.228174" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.268562" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.270002" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.433502" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.78,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.91,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-11.01,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7,58.13)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-2.88,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.364747" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.955748" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.169498" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.332996" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,36.18,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,41.03,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,55.93,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,59.94,58.13)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,64.04,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> }</t年代p一个n></text> </g> </g> </svg>第二个签名<年代vg height="7.1374998" id="M24" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>集群。让<年代vg height="16.512501" id="M25" style="vertical-align:-4.77652pt;width:59.525002px;" version="1.1" viewbox="0 0 59.525002 16.512501" width="59.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.340701" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.38109" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.544588" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.75,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-28.6,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>是地面距离矩阵,<年代vg height="16.637501" id="M26" style="vertical-align:-4.77652pt;width:86.362503px;" version="1.1" viewbox="0 0 86.362503 16.637501" width="86.362503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.3,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.68,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.691984" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.855484" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.49,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-11.55,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.12,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>地面集群之间的距离吗<年代vg height="11.05" id="M27" style="vertical-align:-3.2316pt;width:11.7875px;" version="1.1" viewbox="0 0 11.7875 11.05" width="11.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="12.975" id="M28" style="vertical-align:-4.77652pt;width:12.8125px;" version="1.1" viewbox="0 0 12.8125 12.975" width="12.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.22,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>我们假设签名<年代vg height="10.325" id="M29" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表示“供应的地方,”签名<年代vg height="12.925" id="M30" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表示“需求的地方,”和地面的距离<年代vg height="16.512501" id="M31" style="vertical-align:-4.77652pt;width:17.375px;" version="1.1" viewbox="0 0 17.375 16.512501" width="17.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.3,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> </g> </g> </svg>表示每个供给和需求之间的运输成本。我们的目标是找到一个流<年代vg height="16.512501" id="M32" style="vertical-align:-4.77652pt;width:57.1875px;" version="1.1" viewbox="0 0 57.1875 16.512501" width="57.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.190185" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.230574" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.394073" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.61,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.46,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>这样<年代vg height="16.512501" id="M33" style="vertical-align:-4.77652pt;width:17.737499px;" version="1.1" viewbox="0 0 17.737499 16.512501" width="17.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> </g> </g> </svg>隔<年代vg height="11.05" id="M34" style="vertical-align:-3.2316pt;width:11.7875px;" version="1.1" viewbox="0 0 11.7875 11.05" width="11.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="12.975" id="M35" style="vertical-align:-4.77652pt;width:12.8125px;" version="1.1" viewbox="0 0 12.8125 12.975" width="12.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.22,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,它最小化总成本如下:<年代p一个nclass="equation" id="EEq2"> <svg height="50.275002" id="M36" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.275002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.275)"> <g transform="translate(72,-31.78)"> <text transform="matrix(1,0,0,-1,127.58,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> W</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.390233" y="0"> O</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.417398" y="0"> R</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.756901" y="0"> K</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.859566" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.023064" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.449844" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.663597" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.428436" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.629684" y="0"> F</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.581352" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.220688" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.82,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.85,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.38,35.94)"> <tspan style="font-size: 8.75px; " x="20.52" y="-29.67"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,242,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.92,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,258.16,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,264.81,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.96,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,278.9,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,286.05,48.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="188.07001" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="192.23351" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="198.485" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>方程(<一个href="#EEq2">2</一个>)获得以下约束:<年代p一个nclass="equation" id="EEq3"> <svg height="199.39999" id="M37" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 199.39999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,199.4)"> <g transform="translate(72,87.52)"> <text transform="matrix(1,0,0,-1,128.46,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,135.4,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.02,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.458027" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.185364" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.213249" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.577515" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.617905" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.495033" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.872284" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.59962" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="114.64001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="122.967" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="135.0074" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="141.23" y="1.13"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="328.10001" y="1.13"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="332.26349" y="1.13"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="338.51498" y="1.13"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.78,43.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,142.88,20.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.06,13.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,159.03,27.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,165.97,23.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.59,27.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,198.32,23.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.6,21.76)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.54,27.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.893473" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.92136" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.285625" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.326015" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.203148" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="268.57999" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="272.7435" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="278.995" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.39,-6.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,143.42,-28.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.95,-35.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,159.58,-22.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.52,-25.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.14,-22.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,198.87,-25.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.88,-27.33)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,206.68,-22.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.893473" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.92136" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.26086" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.30125" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.51524" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="267.44" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="271.60349" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="277.85501" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,122.95,-53.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,117.98,-76.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,119.51,-83.36)"> <tspan style="font-size: 8.75px; " x="20.530001" y="-29.67"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,134.13,-76.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,136.05,-83.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.29,-69.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.23,-72.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,167.85,-69.63)"> <tspan style="font-size: 12.50px; " x="35.66" y="9.7399998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.231054" y="0"> n</t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.58,-53.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,213.61,-76.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,215.14,-83.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,229.77,-69.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.46,-72.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.74,-74.95)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,246.68,-69.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n></text> <text transform="matrix(1,0,0,-1,257.79,-53.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,251.89,-76.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,253.08,-83.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,268.04,-69.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,277.73,-72.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,281.74,-74.95)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,285.54,-79.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.19" y="-9.7399998"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="188.58" y="-8.8699999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="192.7435" y="-8.8699999"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="198.995" y="-8.8699999"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>约束(<一个href="#EEq3">3</一个>)允许的运动用品<年代vg height="10.325" id="M41" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>来<年代vg height="12.925" id="M42" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>而不是反之亦然。约束(<一个href="#EEq3">4</一个>)限制供应的数量,可以发送的集群<年代vg height="10.325" id="M43" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>他们的重量。约束(<一个href="#EEq3">5</一个>)限制了集群<年代vg height="12.925" id="M44" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>所以供应不超过权重约束(<一个href="#EEq3">6</一个>)部队最大可能数量的供应可能动摇。这被称为<我>总流</我>。运输问题一旦解决,我们已经找到了最优流<年代vg height="10.325" id="M45" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,EMD被定义为总流产生的工作规范化<年代p一个nclass="equation" id="EEq7"> <svg height="39.962502" id="M46" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.962502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,39.9625)"> <g transform="translate(72,-40.03)"> <text transform="matrix(1,0,0,-1,126.19,55.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.857164" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.020664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.447445" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.648693" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.413536" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.052872" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.300003" y="-8.2200003"> W</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.690231" y="-8.2200003"> O</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.7174" y="-8.2200003"> R</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="106.0569" y="-8.2200003"> K</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="117.15956" y="-8.2200003"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="121.32307" y="-8.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="128.74985" y="-8.2200003"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="133.96359" y="-8.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="143.72844" y="-8.2200003"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="148.92969" y="-8.2200003"> F</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="155.88135" y="-8.2200003"> )</t年代p一个n></text> <g> <path d="m 203.49,58.4 82.75,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,212.46,45.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代p一个n></text> <text transform="matrix(1,0,0,-1,223.89,51.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.48,45.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代p一个n></text> <text transform="matrix(1,0,0,-1,248.91,51.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,263.18,45.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,270.12,42.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,287.44,55.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="186.67999" y="2.3800001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="190.84351" y="2.3800001"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="197.095" y="2.3800001"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>一个二维的例子EMD。签名<年代vg height="10.55" id="M47" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>供应表所示<一个href="//www.newsama.com/journals/am/2011/421820/tab1/" target="_blank">1</一个>,签名<年代vg height="10.325" id="M48" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>作为要求如表所示<一个href="//www.newsama.com/journals/am/2011/421820/tab2/" target="_blank">2</一个>。我们假设是欧几里得距离地面的距离。签名之间的运输成本<年代vg height="10.55" id="M49" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="10.325" id="M50" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>计算如表所示<一个href="//www.newsama.com/journals/am/2011/421820/tab3/" target="_blank">3</一个>。通过求解运输问题在上述条件下,我们可以获得优化交通流和体重,如图<一个href="//www.newsama.com/journals/am/2011/421820/fig2/" target="_blank">2</一个>。</p><d我vclass="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr class="thead"> <td align="left"></td> <td align="center">重量</td><td一个lign="center"><span style="width: 8.7250004px;"> <svg height="7.1624999" id="M52" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 7.875px;"> <svg height="9.8625002" id="M53" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg></span></td> </tr> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr> <td align="left"><span style="width: 17.424999px;"> <svg height="14.6125" id="M54" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 17.424999 14.6125" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6125)"> <g transform="translate(72,-60.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.3</td><td一个lign="center">5</td><td一个lign="center">5</td></tr><tr> <td align="left"><span style="width: 17.424999px;"> <svg height="14.4625" id="M55" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.424999 14.4625" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.3</td><td一个lign="center">0</td><td一个lign="center">5</td></tr><tr> <td align="left"><span style="width: 17.424999px;"> <svg height="14.4625" id="M56" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.424999 14.4625" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.3</td><td一个lign="center">0</td><td一个lign="center">0</td></tr><tr> <td align="left"><span style="width: 17.424999px;"> <svg height="14.6125" id="M57" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 17.424999 14.6125" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6125)"> <g transform="translate(72,-60.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.3</td><td一个lign="center">5</td><td一个lign="center">0</td></tr><tr class="table-tr"> <td colspan="4"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 签名的一个例子<年代vg height="10.55" id="M51" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</d我v></d我v></d我v><d我v class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-content fig-content-tab2"> <table class="table-group" id="tab2"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr class="thead"> <td align="left"></td> <td align="center">重量</td><td一个lign="center"><span style="width: 8.7250004px;"> <svg height="7.1624999" id="M59" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 7.875px;"> <svg height="9.8625002" id="M60" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg></span></td> </tr> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr> <td align="left"><span style="width: 17.1px;"> <svg height="14.3875" id="M61" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 17.1 14.3875" width="17.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.4</td><td一个lign="center">1</td><td一个lign="center">1</td></tr><tr> <td align="left"><span style="width: 17.1px;"> <svg height="14.2375" id="M62" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.1 14.2375" width="17.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.4</td><td一个lign="center">4</td><td一个lign="center">1</td></tr><tr> <td align="left"><span style="width: 17.1px;"> <svg height="14.2375" id="M63" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.1 14.2375" width="17.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.4</td><td一个lign="center">2。5</td><td一个lign="center">4</td></tr><tr class="table-tr"> <td colspan="4"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 签名的一个例子<年代vg height="10.325" id="M58" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</d我v></d我v></d我v><d我v class="floats-partial-section partial-other-wrapper" data-section="tab3"> <div class="floats-partial-content fig-content-tab3"> <table class="table-group" id="tab3"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr class="thead"> <td align="left"></td> <td align="center"><span style="width: 17.1px;"> <svg height="14.3875" id="M66" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 17.1 14.3875" width="17.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 17.1px;"> <svg height="14.2375" id="M67" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.1 14.2375" width="17.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 17.1px;"> <svg height="14.2375" id="M68" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.1 14.2375" width="17.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg></span></td> </tr> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr> <td align="left"><span style="width: 17.424999px;"> <svg height="14.6125" id="M69" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 17.424999 14.6125" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6125)"> <g transform="translate(72,-60.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">5.6569</td><td一个lign="center">4.1231</td><td一个lign="center">2.6926</td></tr><tr> <td align="left"><span style="width: 17.424999px;"> <svg height="14.4625" id="M70" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.424999 14.4625" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">4.1231</td><td一个lign="center">5.6569</td><td一个lign="center">2.6926</td></tr><tr> <td align="left"><span style="width: 17.424999px;"> <svg height="14.4625" id="M71" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.424999 14.4625" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">1.4142</td><td一个lign="center">4.1231</td><td一个lign="center">4.7170</td></tr><tr> <td align="left"><span style="width: 17.424999px;"> <svg height="14.6125" id="M72" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 17.424999 14.6125" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6125)"> <g transform="translate(72,-60.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">4.1231</td><td一个lign="center">1.4142</td><td一个lign="center">4.7170</td></tr><tr class="table-tr"> <td colspan="4"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表3</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/tab3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 成本矩阵的签名<年代vg height="10.55" id="M64" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="10.325" id="M65" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</d我v></d我v></d我v><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.002" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.002.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 优化流程。</t一个ble> </div> </div> </div> <p>在图<一个href="//www.newsama.com/journals/am/2011/421820/fig2/" target="_blank">2</一个>,白色的圆圈表示供应的地方,黑色的圆圈表示需求的地方。圈内的数字表示的重量供应或需求。箭头显示交通流和箭头旁边的数字表示运输重量。图的流总成本<一个href="//www.newsama.com/journals/am/2011/421820/fig2/" target="_blank">2</一个>得到如下:<年代p一个nclass="equation" id="eq1"> <svg height="15.75" id="M73" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 15.75" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.75)"> <g transform="translate(72,-59.4)"> <text transform="matrix(1,0,0,-1,67.17,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.37869" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.542189" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.79369" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.919439" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.946606" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.29813" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.549629" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.675381" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.92688" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.178375" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.429878" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.469551" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.809769" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="99.061272" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.18702" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="111.21419" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="117.56571" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="123.81721" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="126.94296" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="133.19446" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="139.44595" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="145.69746" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="154.73712" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="166.07735" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="172.32884" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="175.45461" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="184.48177" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="190.83328" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="197.08479" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="200.21054" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="206.46204" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="212.71353" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.96504" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.21654" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="232.85587" y="0"> ≈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="244.89626" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="251.14777" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="254.27351" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="260.52502" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="266.77652" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="273.02802" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="279.27951" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="406.95001" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="411.11349" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="417.36499" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>运输问题的计算复杂度是基于单纯形算法,一个指数最坏情况。</p><h5 id="sec2.3">2.3。图像检索使用EMD</h5> <p>颜色分布数据申请CBIR模型是从彩色分割图像中提取的。如图<一个href="//www.newsama.com/journals/am/2011/421820/fig3/" target="_blank">3</一个>分布包括重量、流动成本,和图像功能。重量是像素的数量在每一个地区。每个分布的流动成本可以通过计算获得图像特征之间的欧几里得距离在每个地区。每个区域的图像特征是由中心的位置<年代vg height="13.55" id="M74" style="vertical-align:-2.29482pt;width:38.599998px;" version="1.1" viewbox="0 0 38.599998 13.55" width="38.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.404896" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.606384" y="0"> )</t年代p一个n></text> </g> </g> </svg>和平均颜色签名(RGB)。图<一个href="//www.newsama.com/journals/am/2011/421820/fig4/" target="_blank">4</一个>使用EMD检索结果的显示了一个示例,在这个示例检索结果从10000年图像数据集。另一方面,数字<一个href="//www.newsama.com/journals/am/2011/421820/fig5/" target="_blank">5</一个>显示了一个示例使用的检索结果<年代vg height="14.2375" id="M75" style="vertical-align:-3.13504pt;width:17.2875px;" version="1.1" viewbox="0 0 17.2875 14.2375" width="17.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>从相同的数据集。从这些结果,可以发现,使用EMD CBIR系统能够反映人类的知觉相似性。</p><d我vclass="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.003" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.003.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 颜色对EMD签名。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.004" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.004.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 使用EMD示例的检索结果。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.005" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.005.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="16.237499" id="M76" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 17.1625 16.237499" width="17.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2375)"> <g transform="translate(72,-59.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <table> 使用示例的检索结果。</t一个ble> </div> </div> </div> <h4 id="emd-lower-bound">3所示。EMD下界</h4> <h5 id="sec3.1">3.1。基本定义和符号</h5> <p>我们表示一个签名<年代vg height="7.1624999" id="M77" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>如下:<年代p一个nclass="equation" id="eq2"> <svg height="48.799999" id="M78" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.799999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.8)"> <g transform="translate(72,-32.96)"> <text transform="matrix(1,0,0,-1,107.99,61.13)"> <tspan style="font-size: 12.50px; " x="35.419998" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.379999" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.569225" y="2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.29,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,155.16,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.06,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.94,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.14" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.81,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.69,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.59,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.46,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.939999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.790001" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.141248" y="-2.51"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.719746" y="-2.51"> ,</t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.13,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,275.98,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,290.88,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,295.72,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-177.38" y="21.860001"> ≡</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-163.26411" y="21.860001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-159.10062" y="21.860001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-149.22325" y="21.860001"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-144.022" y="21.860001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-134.33217" y="21.860001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-126.69284" y="21.860001"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-114.65245" y="21.860001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,191.14,41.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.656064" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8440642" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.83,36.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="271.29001" y="-12.59"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="275.45349" y="-12.59"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="281.70499" y="-12.59"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代p一个nclass="equation" id="eq3"> <svg height="19.387501" id="M79" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.3875)"> <g transform="translate(72,-56.49)"> <text transform="matrix(1,0,0,-1,127.97,61.1)"> <tspan style="font-size: 12.50px; " x="22.389999" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.18" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.352484" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.03,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,168.98,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋯</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.665779" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,189.52,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,194.37,58.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.2600002" y="-2.51"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.287886" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,223.92,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.257344" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.03,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.331799" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.359684" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.611183" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="228.84" y="-0.02"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="233.00349" y="-0.02"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.255" y="-0.02"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="245.5065" y="-0.02"> )</t年代p一个n></text> </g> </g> </svg></span>在这里,<年代vg height="10.75" id="M80" style="vertical-align:-0.15048pt;width:9.375px;" version="1.1" viewbox="0 0 9.375 10.75" width="9.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>集群的尺寸吗<年代vg height="17.7125" id="M81" style="vertical-align:-3.2316pt;width:50.799999px;" version="1.1" viewbox="0 0 50.799999 17.7125" width="50.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.7125)"> <g transform="translate(72,-57.83)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.38,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.09,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="7.1374998" id="M82" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是集群的数量。签名的总重量<年代vg height="7.1624999" id="M83" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是<年代p一个nclass="equation" id="eq4"> <svg height="50.275002" id="M84" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.275002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.275)"> <g transform="translate(72,-31.78)"> <text transform="matrix(1,0,0,-1,176.1,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.79,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,195.22,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,213.16,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.26,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,208.45,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,223.41,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,233.1,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.53,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="230.34" y="0.91000003"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="234.50349" y="0.91000003"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="240.755" y="0.91000003"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="247.0065" y="0.91000003"> )</t年代p一个n></text> </g> </g> </svg></span>在的情况下<年代vg height="10.7375" id="M85" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>最近的邻居搜索任务,让<年代vg height="7.0124998" id="M86" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>被查询图像和之间的距离<年代vg height="10.7375" id="M87" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在搜索过程中候选人数据。</p><h5 id="sec3.2">3.2。Centroid-Based下界</h5> <p>的重心<年代vg height="12.3125" id="M88" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 12.3125" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3125)"> <g transform="translate(72,-62.15)"> <g> <path d="m -71.95,70.71 6.88,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的签名<年代vg height="16.450001" id="M89" style="vertical-align:-2.21957pt;width:116.075px;" version="1.1" viewbox="0 0 116.075 16.450001" width="116.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.45)"> <g transform="translate(72,-58.84)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.543869" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.421238" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.634991" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.324814" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.951645" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.992035" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,9.12,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.656064" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8440642" y="0"> </t年代p一个n></text> </g> </g> </svg>被定义为<年代p一个nclass="equation" id="EEq8"> <svg height="41.775002" id="M90" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.775002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.775)"> <g transform="translate(72,-38.58)"> <g> <path d="m 168.86,58.91 6.88,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,168.86,50.51)"> <tspan style="font-size: 12.50px; " x="23.58" y="-11.32"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.87,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.15,61.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.84,58.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.26,61.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.14,58.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 192.44,53.63 51.13,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,210.18,41.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,219.87,38.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,244.76,50.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="223.11" y="-1.65"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="227.2735" y="-1.65"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="233.52499" y="-1.65"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.7765" y="-1.65"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p><span class="statement" id="thm1"><span class="statement-title">定理1。</年代p一个n><我>假设<年代vg height="16.450001" id="M91" style="vertical-align:-2.21957pt;width:118.4px;" version="1.1" viewbox="0 0 118.4 16.450001" width="118.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.45)"> <g transform="translate(72,-58.84)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.543869" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.421238" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.634991" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.324814" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.951645" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.992035" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,9.12,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.656064" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8440642" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="16.549999" id="M92" style="vertical-align:-2.29482pt;width:106.5375px;" version="1.1" viewbox="0 0 106.5375 16.549999" width="106.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.55)"> <g transform="translate(72,-58.76)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.868708" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.557812" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.771564" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.697987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.324814" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.365204" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.49,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.656064" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8440642" y="0"> </t年代p一个n></text> </g> </g> </svg>的签名等于总重量<年代vg height="11.225" id="M93" style="vertical-align:-3.13504pt;width:53.9375px;" version="1.1" viewbox="0 0 53.9375 11.225" width="53.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.225)"> <g transform="translate(72,-63.02)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.83,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.86,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> </g> </g> </svg>。然后,</我><年代p一个nclass="equation" id="EEq9"> <svg height="16.862499" id="M94" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.862499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8625)"> <g transform="translate(72,-58.51)"> <text transform="matrix(1,0,0,-1,106.51,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,134.29,59.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> C</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.837584" y="0"> B</t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.55,62.32)"> <tspan style="font-size: 12.50px; " x="42.130001" y="-0.47999999"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.130001" y="0.50999999"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.241398" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.442884" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.082218" y="0"> =</t年代p一个n></text> <g> <path d="m 197.22,70.71 6.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,197.22,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6398134" y="0"> −</t年代p一个n></text> <g> <path d="m 218.21,70.7 6.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,218.21,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.21" y="-0.49000001"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.21" y="0.5"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.299999" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.327887" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.96722" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.082386" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.197552" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.361053" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.237701" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.451454" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.652939" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.891937" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="249.66" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="253.8235" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="260.07501" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="266.32651" y="0"> )</t年代p一个n></text> </g> </g> </svg></span><i>在这里,地面的距离<年代vg height="13.8625" id="M95" style="vertical-align:-2.37006pt;width:27.887501px;" version="1.1" viewbox="0 0 27.887501 13.8625" width="27.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3147354" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.666259" y="0"> 为</t年代p一个n></text> </g> </g> </svg>是任何<年代vg height="16.237499" id="M96" style="vertical-align:-4.74141pt;width:17.1625px;" version="1.1" viewbox="0 0 17.1625 16.237499" width="17.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2375)"> <g transform="translate(72,-59.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>规范用来测量<年代vg height="16.637501" id="M97" style="vertical-align:-4.77652pt;width:51.262501px;" version="1.1" viewbox="0 0 51.262501 16.637501" width="51.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.815095" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.26,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.63,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>,如科恩和所述Guibas [<一个href="#B4">4</一个>]。</我></年代p一个n></p> <h5 id="sec3.3">3.3。计算不使用<年代vg height="14.375" id="M98" style="vertical-align:-3.24037pt;width:55.349998px;" version="1.1" viewbox="0 0 55.349998 14.375" width="55.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.9271421" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.492657" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.58,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.872592" y="0"> </t年代p一个n></text> </g> </g> </svg></h5> <p>计算的<年代vg height="14.5375" id="M99" style="vertical-align:-3.25792pt;width:50.075001px;" version="1.1" viewbox="0 0 50.075001 14.5375" width="50.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5375)"> <g transform="translate(72,-60.37)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> C</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.837584" y="0"> B</t年代p一个n></text> </g> </g> </svg>,Ajiok中描述的方法等。<一个href="#B8">8</一个>可以跳过应用其计算步骤,因为<年代vg height="14.5375" id="M100" style="vertical-align:-3.25792pt;width:50.075001px;" version="1.1" viewbox="0 0 50.075001 14.5375" width="50.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5375)"> <g transform="translate(72,-60.37)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> C</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.837584" y="0"> B</t年代p一个n></text> </g> </g> </svg>是<年代vg height="14.2375" id="M101" style="vertical-align:-3.13504pt;width:17.2875px;" version="1.1" viewbox="0 0 17.2875 14.2375" width="17.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>每一个签名的质心之间的距离。该方法作为每个质心的计算每个维度的sigunature向量。</p><p>一个例子所示的签名<年代vg height="10.55" id="M102" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>(表<一个href="//www.newsama.com/journals/am/2011/421820/tab1/" target="_blank">1</一个>)查询,签名之间的距离<年代vg height="10.6125" id="M103" style="vertical-align:-0.15048pt;width:11.8625px;" version="1.1" viewbox="0 0 11.8625 10.6125" width="11.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6125)"> <g transform="translate(72,-63.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>(表<一个href="//www.newsama.com/journals/am/2011/421820/tab4/" target="_blank">4</一个>)和查询计算<年代vg height="7.0124998" id="M104" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>设置为1.5。然后,通过以下质心(<一个href="#EEq8">12</一个>):<年代p一个nclass="equation" id="eq10"> <svg height="51.75" id="M105" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 51.75" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,51.75)"> <g transform="translate(72,-30.6)"> <g> <path d="m 172.18,70.71 8.96,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,172.18,59.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.427982" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.469999" y="-0.0099999998"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.633499" y="-0.0099999998"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.884998" y="-0.0099999998"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.01075" y="-0.0099999998"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.262249" y="-0.0099999998"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.463497" y="-0.0099999998"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.714996" y="-0.0099999998"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.840748" y="-0.0099999998"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.092247" y="-0.0099999998"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.34375" y="-0.0099999998"> ,</t年代p一个n></text> <g> <path d="m 168.84,45.53 9.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,168.84,34.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.853084" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.893473" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.056973" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.308472" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.434223" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.685722" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.899471" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.150974" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.276722" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.528221" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.779724" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.018723" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="299.03" y="-13.77"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="303.19351" y="-13.77"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="309.44501" y="-13.77"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="315.6965" y="-13.77"> )</t年代p一个n></text> </g> </g> </svg></span>首先,<年代vg height="14.2375" id="M106" style="vertical-align:-3.13504pt;width:17.2875px;" version="1.1" viewbox="0 0 17.2875 14.2375" width="17.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>距离第一个维重心计算如下:<年代p一个nclass="equation" id="eq11"> <svg height="18.862499" id="M107" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.862499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.8625)"> <g transform="translate(72,-56.91)"> <text transform="matrix(1,0,0,-1,146.08,60.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,151.18,65.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,159.53,60.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.405136" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.383968" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.424358" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.587856" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.839359" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.965107" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.992271" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.332497" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="89.583992" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.709747" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="98.961243" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,262.67,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,267.54,60.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="200.33" y="-0.62"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="204.4935" y="-0.62"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="210.745" y="-0.62"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="216.99651" y="-0.62"> )</t年代p一个n></text> </g> </g> </svg></span>第一个维度的距离大于<年代vg height="13.775" id="M108" style="vertical-align:-0.0pt;width:12.6px;" version="1.1" viewbox="0 0 12.6 13.775" width="12.6" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.775)"> <g transform="translate(72,-60.98)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.85,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>;因此,计算步骤之后第二个维度可以被消除。</p><d我vclass="floats-partial-section partial-other-wrapper" data-section="tab4"> <div class="floats-partial-content fig-content-tab4"> <table class="table-group" id="tab4"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr class="thead"> <td align="left"></td> <td align="center">重量</td><td一个lign="center"><span style="width: 8.7250004px;"> <svg height="7.1624999" id="M110" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 7.875px;"> <svg height="9.8625002" id="M111" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg></span></td> </tr> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr> <td align="left"><span style="width: 16.700001px;"> <svg height="14.4875" id="M112" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 16.700001 14.4875" width="16.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4875)"> <g transform="translate(72,-60.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.5</td><td一个lign="center">5</td><td一个lign="center">5</td></tr><tr> <td align="left"><span style="width: 16.700001px;"> <svg height="14.3375" id="M113" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 16.700001 14.3375" width="16.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.5</td><td一个lign="center">5</td><td一个lign="center">0</td></tr><tr> <td align="left"><span style="width: 16.700001px;"> <svg height="14.3375" id="M114" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 16.700001 14.3375" width="16.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">0.2</td><td一个lign="center">2</td><td一个lign="center">7</td></tr><tr class="table-tr"> <td colspan="4"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表4</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/tab4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 签名的一个例子<年代vg height="10.6125" id="M109" style="vertical-align:-0.15048pt;width:11.8625px;" version="1.1" viewbox="0 0 11.8625 10.6125" width="11.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6125)"> <g transform="translate(72,-63.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</d我v></d我v></d我v><h5 id="sec3.4">3.4。独立最小化下界</h5> <p> <svg height="14.5375" id="M115" style="vertical-align:-3.25792pt;width:50.075001px;" version="1.1" viewbox="0 0 50.075001 14.5375" width="50.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5375)"> <g transform="translate(72,-60.37)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> C</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.837584" y="0"> B</t年代p一个n></text> </g> </g> </svg>表示为基础的下界<年代vg height="16.237499" id="M116" style="vertical-align:-4.74141pt;width:17.1625px;" version="1.1" viewbox="0 0 17.1625 16.237499" width="17.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2375)"> <g transform="translate(72,-59.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>距离。另一方面,同意et al。<一个href="#B5">5</一个>)提出了独立最小化下界基于cross-bin不同措施。</p><p><年代p一个nclass="statement" id="thm2"><span class="statement-title">定理2。</年代p一个n><我>假设<年代vg height="16.450001" id="M117" style="vertical-align:-2.21957pt;width:118.4px;" version="1.1" viewbox="0 0 118.4 16.450001" width="118.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.45)"> <g transform="translate(72,-58.84)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.543869" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.421238" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.634991" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.324814" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.951645" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.992035" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,9.12,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.656064" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8440642" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="16.549999" id="M118" style="vertical-align:-2.29482pt;width:106.5375px;" version="1.1" viewbox="0 0 106.5375 16.549999" width="106.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.55)"> <g transform="translate(72,-58.76)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.868708" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.557812" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.771564" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.697987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.324814" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.365204" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.49,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.656064" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8440642" y="0"> </t年代p一个n></text> </g> </g> </svg>的签名等于总重量<年代vg height="11.225" id="M119" style="vertical-align:-3.13504pt;width:53.9375px;" version="1.1" viewbox="0 0 53.9375 11.225" width="53.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.225)"> <g transform="translate(72,-63.02)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.83,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.86,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> </g> </g> </svg>。然后,</我><年代p一个nclass="equation" id="EEq10"> <svg height="77.199997" id="M120" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 77.199997" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,77.2)"> <g transform="translate(72,-10.24)"> <text transform="matrix(1,0,0,-1,104.2,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,131.98,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 米</t年代p一个n></text> <text transform="matrix(1,0,0,-1,145.26,49.61)"> <tspan style="font-size: 12.50px; " x="65.739998" y="9.7399998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.241398" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.442884" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.082218" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.110104" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.837437" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.313271" y="0"> n</t年代p一个n></text> <text transform="matrix(1,0,0,-1,226.08,65.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,221.11,43.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,222.64,35.87)"> <tspan style="font-size: 8.75px; " x="20.52" y="-29.67"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.26,43.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.18,35.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.61,60.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.26,57.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <g> <path d="m 254.61,52.73 13.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,254.67,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.94" y="-8.75"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,276.55,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,283.7,39.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-108.36" y="25.83"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-96.319611" y="25.83"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-88.680275" y="25.83"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-77.565109" y="25.83"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-66.462448" y="25.83"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-62.298946" y="25.83"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-55.422298" y="25.83"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-50.208546" y="25.83"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-44.007057" y="25.83"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-37.755558" y="25.83"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="184.17" y="1.88"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="188.3335" y="1.88"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="194.58499" y="1.88"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="200.8365" y="1.88"> )</t年代p一个n></text> </g> </g> </svg></span><i>方程(<一个href="#EEq10">16</一个>)获得以下约束:</我><年代p一个nclass="equation" id="EEq11"> <svg height="167.9875" id="M121" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 167.9875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,167.9875)"> <g transform="translate(72,62.39)"> <text transform="matrix(1,0,0,-1,128.46,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,135.4,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.02,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.458027" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.185364" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.213249" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.577515" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.617905" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.495033" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.872284" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.59962" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="114.64001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="122.967" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="135.0074" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="141.23" y="1.13"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="321.85001" y="1.13"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="326.01349" y="1.13"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="332.26498" y="1.13"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="338.51651" y="1.13"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.78,43.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.88,20.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.06,13.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.03,27.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,167.97,23.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.59,27.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.32,23.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.54,27.07)"> <tspan style="font-size: 12.50px; " x="-16.700001" y="35.560001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.893473" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.92136" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.285625" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.326015" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.203148" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="264.32999" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="268.4935" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="274.745" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="280.99649" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,193.77,-11.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.4,-8.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,222.36,-11.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,226.79,-8.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="241.08" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="245.2435" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="251.495" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="257.74649" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,160.35,-28.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,155.38,-51.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,156.91,-58.23)"> <tspan style="font-size: 8.75px; " x="20.52" y="-29.68"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,171.53,-51.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,173.45,-58.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.69,-44.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,194.63,-47.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.25,-44.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,226.98,-47.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.41,-44.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.37,-47.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,260.33,-44.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="207.53999" y="0.91000003"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.70351" y="0.91000003"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.955" y="0.91000003"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.2065" y="0.91000003"> )</t年代p一个n></text> </g> </g> </svg></span><i><span class="displayed-label" id="EEq12"></span><span class="displayed-label" id="EEq13"></span><span class="displayed-label" id="EEq14"></span>在哪里<年代vg height="16.512501" id="M125" style="vertical-align:-4.77652pt;width:17.737499px;" version="1.1" viewbox="0 0 17.737499 16.512501" width="17.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> </g> </g> </svg>是流<年代vg height="11.05" id="M126" style="vertical-align:-3.2316pt;width:12.75px;" version="1.1" viewbox="0 0 12.75 11.05" width="12.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>来<年代vg height="12.95" id="M127" style="vertical-align:-4.77652pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 12.95" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.95)"> <g transform="translate(72,-61.64)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="16.637501" id="M128" style="vertical-align:-4.77652pt;width:87.912498px;" version="1.1" viewbox="0 0 87.912498 16.637501" width="87.912498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.3,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.68,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.691984" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.855484" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-24.95,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.73,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-10.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-5.89,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>地面集群之间的距离吗<年代vg height="11.05" id="M129" style="vertical-align:-3.2316pt;width:12.75px;" version="1.1" viewbox="0 0 12.75 11.05" width="12.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="12.95" id="M130" style="vertical-align:-4.77652pt;width:13.4125px;" version="1.1" viewbox="0 0 13.4125 12.95" width="13.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.95)"> <g transform="translate(72,-61.64)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="19.4125" id="M131" style="vertical-align:-5.35329pt;width:189.425px;" version="1.1" viewbox="0 0 189.425 19.4125" width="189.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.4125)"> <g transform="translate(72,-56.47)"> <text transform="matrix(1,0,0,-1,-71.95,61.86)"> <tspan style="font-size: 12.50px; " x="28.08" y="0.029999999"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.028847" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.45,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-18.85,61.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.43,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,6.85,61.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,13.79,58.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,24.41,61.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,46.14,58.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,55.57,61.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,73.53,58.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Σ</t年代p一个n></text> </g> </g> </svg>。</我></年代p一个n></p> <h5 id="sec3.5">3.5。计算不使用<年代vg height="14.2375" id="M132" style="vertical-align:-3.13504pt;width:57.1875px;" version="1.1" viewbox="0 0 57.1875 14.2375" width="57.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.9271421" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.492657" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.58,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.2009602" y="0"> </t年代p一个n></text> </g> </g> </svg></h5> <p>的计算成本<年代vg height="14.375" id="M133" style="vertical-align:-3.13504pt;width:48.837502px;" version="1.1" viewbox="0 0 48.837502 14.375" width="48.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 米</t年代p一个n></text> </g> </g> </svg>可以减少削弱运输问题的约束。在图<一个href="//www.newsama.com/journals/am/2011/421820/fig2/" target="_blank">2</一个>,总流等于总重量(供应或需求),因为(的约束<一个href="#EEq3">4</一个>)和(<一个href="#EEq3">5</一个>)感到满意。之间的差异<年代vg height="14.375" id="M134" style="vertical-align:-3.13504pt;width:48.837502px;" version="1.1" viewbox="0 0 48.837502 14.375" width="48.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 米</t年代p一个n></text> </g> </g> </svg>和正常的EMD约束流的数量,一个集群可以接收。而正常的EMD需要流向某一集群的总和等于集群(的重量<一个href="#EEq12">18</一个>),<年代vg height="14.375" id="M135" style="vertical-align:-3.13504pt;width:48.837502px;" version="1.1" viewbox="0 0 48.837502 14.375" width="48.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 米</t年代p一个n></text> </g> </g> </svg>只有确保任何单个集群,传入流的重量不超过集群(<一个href="#EEq13">19</一个>);也就是说,总流到一个集群可以超过它的重量。最后的流<年代vg height="14.6" id="M136" style="vertical-align:-3.13504pt;width:87.849998px;" version="1.1" viewbox="0 0 87.849998 14.6" width="87.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 米</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.97,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.12815" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.329397" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.031487" y="0"> )</t年代p一个n></text> </g> </g> </svg>如表所示<一个href="//www.newsama.com/journals/am/2011/421820/tab5/" target="_blank">5</一个>总流<年代vg height="14.2375" id="M137" style="vertical-align:-3.13504pt;width:17.1px;" version="1.1" viewbox="0 0 17.1 14.2375" width="17.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>超过<年代vg height="13.95" id="M138" style="vertical-align:-5.32956pt;width:25px;" version="1.1" viewbox="0 0 25 13.95" width="25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.95)"> <g transform="translate(72,-60.84)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.17,60.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。</p><d我vclass="floats-partial-section partial-other-wrapper" data-section="tab5"> <div class="floats-partial-content fig-content-tab5"> <table class="table-group" id="tab5"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr> <td align="left"></td> <td align="center"><span style="width: 25px;"> <svg height="14.0625" id="M140" style="vertical-align:-5.41734pt" version="1.1" viewbox="0 0 25 14.0625" width="25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.17,60.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 25px;"> <svg height="13.95" id="M141" style="vertical-align:-5.32956pt" version="1.1" viewbox="0 0 25 13.95" width="25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.95)"> <g transform="translate(72,-60.84)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.17,60.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 25px;"> <svg height="13.95" id="M142" style="vertical-align:-5.32956pt" version="1.1" viewbox="0 0 25 13.95" width="25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.95)"> <g transform="translate(72,-60.84)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.17,60.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg></span></td> </tr> <tr> <td align="left"></td> <td align="center">0.4</td><td一个lign="center">0.4</td><td一个lign="center">0.4</td></tr><tr> <td align="center" colspan="4"> <hr></td> </tr> <tr> <td align="left"> <svg height="14.0625" id="M143" style="vertical-align:-5.41734pt" version="1.1" viewbox="0 0 25.237499 14.0625" width="25.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.98,60.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>0.3</td><td一个lign="center">0.0000</td><td一个lign="center">0.0000</td><td一个lign="center">0.3000</td></tr><tr> <td align="left"> <svg height="13.95" id="M144" style="vertical-align:-5.32956pt" version="1.1" viewbox="0 0 25.237499 13.95" width="25.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.95)"> <g transform="translate(72,-60.84)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.98,60.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>0.3</td><td一个lign="center">0.0000</td><td一个lign="center">0.0000</td><td一个lign="center">0.3000</td></tr><tr> <td align="left"> <svg height="13.95" id="M145" style="vertical-align:-5.32956pt" version="1.1" viewbox="0 0 25.237499 13.95" width="25.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.95)"> <g transform="translate(72,-60.84)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.98,60.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>0.3</td><td一个lign="center">0.3000</td><td一个lign="center">0.0000</td><td一个lign="center">0.0000</td></tr><tr> <td align="left"> <svg height="14.0625" id="M146" style="vertical-align:-5.41734pt" version="1.1" viewbox="0 0 25.237499 14.0625" width="25.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.98,60.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>0.3</td><td一个lign="center">0.0000</td><td一个lign="center">0.3000</td><td一个lign="center">0.0000</td></tr><tr class="table-tr"> <td colspan="4"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表5</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/tab5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 流<年代vg height="14.375" id="M139" style="vertical-align:-3.13504pt;width:48.837502px;" version="1.1" viewbox="0 0 48.837502 14.375" width="48.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 米</t年代p一个n></text> </g> </g> </svg>。</d我v></d我v></d我v><p>从这个特点,每个供应的流动可以计算集群。计算<年代vg height="14.375" id="M147" style="vertical-align:-3.13504pt;width:48.837502px;" version="1.1" viewbox="0 0 48.837502 14.375" width="48.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 米</t年代p一个n></text> </g> </g> </svg>,Ajiok中描述的方法等。<一个href="#B8">8</一个>)可以应用于跳过每个供应集群的计算步骤。该方法作为每个供应集群的流计算每个维度的特征向量。</p><p>计算跳过的一个例子<年代vg height="14.6" id="M148" style="vertical-align:-3.13504pt;width:87.849998px;" version="1.1" viewbox="0 0 87.849998 14.6" width="87.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.17,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 米</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.97,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.12815" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.329397" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.031487" y="0"> )</t年代p一个n></text> </g> </g> </svg>所示,<年代vg height="7.0124998" id="M149" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>设置为1.5。首先,一个总运输成本的最小值<年代vg height="14.6125" id="M150" style="vertical-align:-3.25793pt;width:17.424999px;" version="1.1" viewbox="0 0 17.424999 14.6125" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6125)"> <g transform="translate(72,-60.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>获得,其价值相比吗<年代vg height="7.0124998" id="M151" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,如下所示:<年代p一个nclass="equation" id="eq12"> <svg height="41.349998" id="M152" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.35)"> <g transform="translate(72,-38.92)"> <text transform="matrix(1,0,0,-1,150.73,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3772497" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.404415" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.007441" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.13319" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.384689" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.636189" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.887691" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.615025" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.655411" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.906914" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="84.032661" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.284164" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="96.53566" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.78716" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="109.03867" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.619999" y="20.48"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.647888" y="20.48"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.749107" y="20.48"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="317.14001" y="10.86"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="321.3035" y="10.86"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="327.55499" y="10.86"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="333.80649" y="10.86"> )</t年代p一个n></text> </g> </g> </svg></span>的价值<年代vg height="14.6125" id="M153" style="vertical-align:-3.25793pt;width:17.424999px;" version="1.1" viewbox="0 0 17.424999 14.6125" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6125)"> <g transform="translate(72,-60.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>小于<年代vg height="7.0124998" id="M154" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>;总运输成本<年代vg height="14.4625" id="M155" style="vertical-align:-3.13504pt;width:17.424999px;" version="1.1" viewbox="0 0 17.424999 14.4625" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>被添加到<年代vg height="14.6125" id="M156" style="vertical-align:-3.25793pt;width:17.424999px;" version="1.1" viewbox="0 0 17.424999 14.6125" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6125)"> <g transform="translate(72,-60.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>如下:<年代p一个nclass="equation" id="eq13"> <svg height="41.349998" id="M157" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.35)"> <g transform="translate(72,-38.92)"> <text transform="matrix(1,0,0,-1,123.35,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3772497" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.62875" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.880251" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.13175" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.383251" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.410416" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.750637" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.002136" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.127884" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.155052" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.519081" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="85.770576" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.896332" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="95.147827" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="101.39933" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="107.65083" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="117.36566" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="129.40605" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="135.65755" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="138.78329" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="145.03481" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="151.2863" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="157.5378" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="163.78931" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="117.38" y="20.48"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="129.40788" y="20.48"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="134.50911" y="20.48"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="344.51999" y="10.86"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="348.6835" y="10.86"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="354.935" y="10.86"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="361.18649" y="10.86"> )</t年代p一个n></text> </g> </g> </svg></span>总价值大于在哪里<年代vg height="7.0124998" id="M158" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>;因此,计算<年代vg height="14.4625" id="M159" style="vertical-align:-3.13504pt;width:17.424999px;" version="1.1" viewbox="0 0 17.424999 14.4625" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.6125" id="M160" style="vertical-align:-3.25793pt;width:17.424999px;" version="1.1" viewbox="0 0 17.424999 14.6125" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6125)"> <g transform="translate(72,-60.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>可以消除。</p><h4 id="fast-retrieval-algorithm-for-the-emd">4所示。快速检索EMD算法</h4> <h5 id="sec4.1">4.1。算法使用下界</h5> <p>在的情况下<年代vg height="10.7375" id="M161" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>最近邻搜索任务,第一次的检索算法<年代vg height="10.7375" id="M162" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像数据图所示<一个href="//www.newsama.com/journals/am/2011/421820/fig6/" target="_blank">6</一个>的检索算法<年代vg height="11.325" id="M163" style="vertical-align:-0.51414pt;width:34.0625px;" version="1.1" viewbox="0 0 34.0625 11.325" width="34.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5522919" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.892513" y="0"> 1</t年代p一个n></text> </g> </g> </svg>图像数据图所示<一个href="//www.newsama.com/journals/am/2011/421820/fig7/" target="_blank">7</一个>。这种方法计算原始EMD第一<年代vg height="10.7375" id="M164" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像数据库中,最大的距离设置为阈值<年代vg height="7.0124998" id="M165" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。这种方法计算低边界距离成功的数据<年代vg height="10.7375" id="M166" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>+ 1的形象。这种方法不计算原始EMD如果边界距离超过阈值越低<年代vg height="7.0124998" id="M167" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,因为真正的EMD不能低于第一<年代vg height="10.7375" id="M168" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像。在所有其他情况下,该方法计算原始EMD,如果真正的EMD低于第一<年代vg height="10.7375" id="M169" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图片,注册一个新的图像,阈值<年代vg height="7.0124998" id="M170" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>重置。</p><d我vclass="floats-partial-section partial-carousel-wrapper" data-section="fig6"> <div class="floats-partial-content fig-content-fig6"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.006" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.006.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="10.7375" id="M171" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <table> 第一个算法图像数据。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig7"> <div class="floats-partial-content fig-content-fig7"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.007" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.007.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="11.325" id="M172" style="vertical-align:-0.51414pt" version="1.1" viewbox="0 0 34.0625 11.325" width="34.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5522919" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.892513" y="0"> 1</t年代p一个n></text> </g> </g> </svg> <table> 算法的图像数据。</t一个ble> </div> </div> </div> <h5 id="sec4.2">4.2。使用优先队列算法</h5> <p>在近邻搜索基于线性搜索,<年代vg height="10.7375" id="M173" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>搜索结果时获得的<年代vg height="10.7375" id="M174" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>特性接近给定的查询。当一个新发现的结果距离搜索功能,小于最大的电流<年代vg height="10.7375" id="M175" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>结果,结果更新。最大距离的数据必须从候选人名单中删除,并必须添加的新结果。这个过程的有效执行提供了通过使用一个数据结构称为一个优先队列。</p><p>有各种各样的实现优先级队列,其中的一个<我>堆</我>。堆结构如图<一个href="//www.newsama.com/journals/am/2011/421820/fig8/" target="_blank">8</一个>。图显示了一个数组作为一个二叉树,使用密钥指定两个低的钥匙。每个键大于其两个子密钥。这样一个数据结构称为完全二叉树;堆被定义为一个完整的二叉树,它被表示为一个数组中所有节点满足堆条件。堆在这里,条件是,在任何一个节点的关键是大于(或等于)的键子节点。如果这堆条件满意,那么最大的关键总是根节点。如图<一个href="//www.newsama.com/journals/am/2011/421820/fig8/" target="_blank">8</一个>,根数为1,其孩子2和3,孩子4、5、6和7,等等。在这样一个代表,一个节点的父<年代vg height="13.3875" id="M176" style="vertical-align:-2.34499pt;width:24.4625px;" version="1.1" viewbox="0 0 24.4625 13.3875" width="24.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.3875)"> <g transform="translate(72,-61.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.303672" y="0"> ]</t年代p一个n></text> </g> </g> </svg>是<年代vg height="13.6125" id="M177" style="vertical-align:-2.34499pt;width:36.612499px;" version="1.1" viewbox="0 0 36.612499 13.6125" width="36.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.303672" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.779507" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.031006" y="0"> ]</t年代p一个n></text> </g> </g> </svg>(小数点如果截断<年代vg height="12.675" id="M178" style="vertical-align:-2.34499pt;width:7.1374998px;" version="1.1" viewbox="0 0 7.1374998 12.675" width="7.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.675)"> <g transform="translate(72,-61.86)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>很奇怪),和它的孩子们<年代vg height="13.6125" id="M179" style="vertical-align:-2.34499pt;width:32.275002px;" version="1.1" viewbox="0 0 32.275002 13.6125" width="32.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.691505" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.555172" y="0"> ]</t年代p一个n></text> </g> </g> </svg>和<年代vg height="13.6125" id="M180" style="vertical-align:-2.34499pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.6125" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.691505" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.330837" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.671059" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.922558" y="0"> ]</t年代p一个n></text> </g> </g> </svg>;因此,父母和孩子可以很容易地确定每一个节点。</p><d我vclass="floats-partial-section partial-carousel-wrapper" data-section="fig8"> <div class="floats-partial-content fig-content-fig8"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.008" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.008.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 堆结构。</t一个ble> </div> </div> </div> <p>当一个新的搜索结果提供了一个距离小于最大的价值在当前结果,堆的根(候选列表)最大的价值被替换为这个新发现的价值。当这个过程会导致违反堆条件下,根价值交换与最大的孩子恢复状态。如果堆条件违反了下一个阶段,类似的操作应用;程序终止如果父母的价值小于两个孩子,或当堆底。这个处理确保数据结构可以被修复,这样每个节点满足堆条件。</p><h4 id="evaluations">5。评估</h4> <h5 id="sec5.1">5.1。实验结果</h5> <p>为了评估这种方法,数据库中的彩色图像的数量从5000增加到50000(5000年增量),检索时间(CPU时间)来搜索排名前十的图像评估。集群的评价维度的数量代表<年代vg height="11.05" id="M181" style="vertical-align:-3.2316pt;width:12.75px;" version="1.1" viewbox="0 0 12.75 11.05" width="12.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>维,我们准备5 - 11维数据作为图像特征。这些实验是模拟使用PowerPC G4 1.5 GHz 1.25 GB的内存。</p><p>实验结果如图<一个href="//www.newsama.com/journals/am/2011/421820/fig9/" target="_blank">9</一个>- - - - - -<一个href="//www.newsama.com/journals/am/2011/421820/fig12/" target="_blank">12</一个>。五维数据所示的实验结果数据<一个href="//www.newsama.com/journals/am/2011/421820/fig9/" target="_blank">9</一个>和<一个href="//www.newsama.com/journals/am/2011/421820/fig10/" target="_blank">10</一个>维,结果11维数据数据所示<一个href="//www.newsama.com/journals/am/2011/421820/fig11/" target="_blank">11</一个>和<一个href="//www.newsama.com/journals/am/2011/421820/fig12/" target="_blank">12</一个>。为了使效果提出的组合方法的理解,数据<一个href="//www.newsama.com/journals/am/2011/421820/fig10/" target="_blank">10</一个>和<一个href="//www.newsama.com/journals/am/2011/421820/fig12/" target="_blank">12</一个>放大图数据吗<一个href="//www.newsama.com/journals/am/2011/421820/fig9/" target="_blank">9</一个>和<一个href="//www.newsama.com/journals/am/2011/421820/fig11/" target="_blank">11</一个>相应的。在这些图表,表示“没有”正常EMD计算,“cb”表示相应的结果使用centroid-based降低边界的距离,“我”表示相应的使用独立的最小化降低边界距离,并“cb_im”表示相应的结果通过结合“cb”和“即时通讯”的方法。此外,“noskip_ *”代表了每个方法获得的价值没有calculation-skipping算法。</p><d我vclass="floats-partial-section partial-carousel-wrapper" data-section="fig9"> <div class="floats-partial-content fig-content-fig9"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.009" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.009.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图9</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig9/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 对五维数据CPU时间。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig10"> <div class="floats-partial-content fig-content-fig10"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.0010" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.0010.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图10</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig10/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> CPU时间在五维数据(放大图)。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig11"> <div class="floats-partial-content fig-content-fig11"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.0011" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.0011.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图11</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig11/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> CPU时间维上11维的数据。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig12"> <div class="floats-partial-content fig-content-fig12"> <div class="partial-carousel--single-image"> <img alt="" name="421820.fig.0012" src="https://static-01.hindawi.com/articles/am/volume-2011/421820/figures/421820.fig.0012.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图12</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/fig12/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> CPU时间维上11维数据(放大图)。</t一个ble> </div> </div> </div> <p>从实验结果可以看出,当彩色图像的数量是50000,有5个尺寸,需要大约2.5秒来检索一个查询的结果图像通过使用正常的EMD计算。下界的组合方法可以获得相同的结果作为正常的EMD大约0.15秒。另一方面,该方法使用calculation-skipping算法只花了0.1秒。</p><h5 id="sec5.2">5.2。相关的工作</h5> <p>提出了一些推导算法的EMD。贝利和沃曼<一个href="#B9">9</一个>]提出的快速算法<年代vg height="15.875" id="M182" style="vertical-align:-0.17555pt;width:34.849998px;" version="1.1" viewbox="0 0 34.849998 15.875" width="34.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.875)"> <g transform="translate(72,-59.3)"> <text transform="matrix(1,0,0,-1,-69.85,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-2.0999999" y="2.6500001"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.5393329" y="2.6500001"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.654499" y="2.6500001"> D</t年代p一个n></text> </g> </g> </svg>凌,冈田克也(<一个href="#B10">10</一个>]提出的快速算法<年代vg height="14.375" id="M183" style="vertical-align:-3.13504pt;width:59.825001px;" version="1.1" viewbox="0 0 59.825001 14.375" width="59.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.781666" y="0"> _</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.033165" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.06,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>。的<年代vg height="15.875" id="M184" style="vertical-align:-0.17555pt;width:34.849998px;" version="1.1" viewbox="0 0 34.849998 15.875" width="34.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.875)"> <g transform="translate(72,-59.3)"> <text transform="matrix(1,0,0,-1,-69.85,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-2.0999999" y="2.6500001"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.5393329" y="2.6500001"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.654499" y="2.6500001"> D</t年代p一个n></text> </g> </g> </svg>可以通过更换获得地面距离的EMD阈值距离。<年代vg height="14.375" id="M185" style="vertical-align:-3.13504pt;width:59.825001px;" version="1.1" viewbox="0 0 59.825001 14.375" width="59.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.781666" y="0"> _</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.033165" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.06,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>是替代地面距离的<年代vg height="14.2375" id="M186" style="vertical-align:-3.13504pt;width:17.2875px;" version="1.1" viewbox="0 0 17.2875 14.2375" width="17.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>距离。这两个<年代vg height="15.875" id="M187" style="vertical-align:-0.17555pt;width:34.849998px;" version="1.1" viewbox="0 0 34.849998 15.875" width="34.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.875)"> <g transform="translate(72,-59.3)"> <text transform="matrix(1,0,0,-1,-69.85,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-2.0999999" y="2.6500001"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.5393329" y="2.6500001"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.654499" y="2.6500001"> D</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.375" id="M188" style="vertical-align:-3.13504pt;width:59.825001px;" version="1.1" viewbox="0 0 59.825001 14.375" width="59.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.781666" y="0"> _</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.033165" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.06,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>不同于原来的EMD。和他们只表明高速计算方法中,阈值和距离<年代vg height="14.2375" id="M189" style="vertical-align:-3.13504pt;width:17.2875px;" version="1.1" viewbox="0 0 17.2875 14.2375" width="17.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>距离被用作地面距离。另一方面,通过使用我们的算法,原始的EMD可以有效地计算。我们的算法的特点是,可以跳过不必要的计算通过使用EMD下界,并加速的角度不同于他们的方法。</p><h5 id="sec5.3">5.3。未来的工作</h5> <p>该方法首先选择<年代vg height="10.7375" id="M190" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像数据库中的数据作为初始检索结果(图<一个href="//www.newsama.com/journals/am/2011/421820/fig6/" target="_blank">6</一个>)。但是,如果有一些异常值<年代vg height="10.7375" id="M191" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像数据,加速的影响将变得更少,因为阈值<年代vg height="7.0124998" id="M192" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>要大得多。然后,查询和之间的距离越小<年代vg height="10.7375" id="M193" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像数据,提高了检索效率。为了解决这个问题,我们正在计划使用层次聚类索引选择初始数据。VP-tree [<一个href="#B11">11</一个>]和M-tree [<一个href="#B12">12</一个>),著名的度量空间指标,可以作为分层聚类索引。通过使用这些指标,适当的初始数据作为第一<年代vg height="10.7375" id="M194" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像数据可以从叶节点获得首次达到检索过程。可以肯定的是,这些数据不是真的是正确的,但可能包括异常值变得相当低。和之间的距离似乎查询和第一<年代vg height="10.7375" id="M195" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像数据就变小了。上面的改进将作为未来工作。</p><p>为了验证层次索引树可以帮助减少离群值的影响<年代vg height="10.7375" id="M196" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>图像,进行了以下初步实验。首先,查询和之间的最大距离100强计算图像数据。这个距离就是所谓的距离<年代ub>前</年代ub>并设置初始阈值<年代vg height="7.0124998" id="M197" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>该方法。接下来,我们获得查询和100之间的最大距离图像数据在叶子节点,这是达到使用VP-tree首次。这个距离是由距离<年代ub>副总裁</年代ub>,并设置初始阈值<年代vg height="12.5625" id="M198" style="vertical-align:-0.0pt;width:10.8375px;" version="1.1" viewbox="0 0 10.8375 12.5625" width="10.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.5625)"> <g transform="translate(72,-61.95)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.85,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在使用VP-tree的改进方法。这些距离计算5查询和图像数据库,是10000年注册的图像数据。初步的实验结果如表所示<一个href="//www.newsama.com/journals/am/2011/421820/tab6/" target="_blank">6</一个>,欧几里德距离作为距离测量,和数量的维度是48。初步的实验结果,发现初始阈值可以设置为使用VP-tree较小值。</p><d我vclass="floats-partial-section partial-other-wrapper" data-section="tab6"> <div class="floats-partial-content fig-content-tab6"> <table class="table-group" id="tab6"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="3"> <hr></td> </tr> <tr class="thead"> <td align="left"></td> <td align="center"><span style="width: 65.949997px;"> <svg height="17.075001" id="M199" style="vertical-align:-5.03984pt" version="1.1" viewbox="0 0 65.949997 17.075001" width="65.949997" 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</svg></span></td> <td align="center"><span style="width: 62.9375px;"> <svg height="17.075001" id="M200" style="vertical-align:-5.03984pt" version="1.1" viewbox="0 0 62.9375 17.075001" width="62.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.075)"> <g transform="translate(72,-58.34)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.490977" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.079338" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.630671" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.88217" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.433502" y="0"> e</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.95,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> v</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> p</t年代p一个n></text> </g> </g> </svg></span></td> </tr> <tr> <td class="thead-hr" colspan="3"> <hr></td> </tr> <tr> <td align="left"><span style="width: 41.599998px;"> <svg height="11.2625" id="M201" style="vertical-align:-3.1726pt" version="1.1" viewbox="0 0 41.599998 11.2625" width="41.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2625)"> <g transform="translate(72,-62.99)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 问</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.0889611" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.340461" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.891792" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.055292" y="0"> y</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.64,63.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">5028.37</td><td一个lign="center">4723.46</td></tr><tr> <td align="left"><span style="width: 41.599998px;"> <svg height="11.2625" id="M202" style="vertical-align:-3.1726pt" version="1.1" viewbox="0 0 41.599998 11.2625" width="41.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2625)"> <g transform="translate(72,-62.99)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 问</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.0889611" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.340461" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.891792" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.055292" y="0"> y</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.64,63.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">5115.23</td><td一个lign="center">2264.38</td></tr><tr> <td align="left"><span style="width: 41.599998px;"> <svg height="11.425" id="M203" style="vertical-align:-3.2955pt" version="1.1" viewbox="0 0 41.599998 11.425" width="41.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.425)"> <g transform="translate(72,-62.86)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 问</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.0889611" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.340461" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.891792" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.055292" y="0"> y</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.64,63.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">4401.71</td><td一个lign="center">1969.05</td></tr><tr> <td align="left"><span style="width: 41.599998px;"> <svg height="11.2625" id="M204" style="vertical-align:-3.1726pt" version="1.1" viewbox="0 0 41.599998 11.2625" width="41.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2625)"> <g transform="translate(72,-62.99)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 问</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.0889611" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.340461" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.891792" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.055292" y="0"> y</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.64,63.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">4071.22</td><td一个lign="center">2437.28</td></tr><tr> <td align="left"><span style="width: 41.599998px;"> <svg height="11.425" id="M205" style="vertical-align:-3.2955pt" version="1.1" viewbox="0 0 41.599998 11.425" width="41.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.425)"> <g transform="translate(72,-62.86)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 问</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.0889611" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.340461" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.891792" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.055292" y="0"> y</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.64,63.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n></text> </g> </g> </svg></span></td> <td align="center">4329.04</td><td一个lign="center">1588.82</td></tr><tr> <td align="center" colspan="3"> <hr></td> </tr> <tr> <td align="left">平均</td><td一个lign="center">4589.11</td><td一个lign="center">2596.60</td></tr><tr class="table-tr"> <td colspan="3"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表6</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/am/2011/421820/tab6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 初步实验结果。</d我v></d我v></d我v><h4 id="conclusion">6。结论</h4> <p>摘要快速检索方法挖土机的距离提出了多媒体数据库。该方法利用EMD的下边界距离,结合calculation-skipping算法。此外,该方法的有效性是由经验观察。为未来的工作,各种多媒体信息检索系统使用快速EMD应该实现。</p><h4 id="acknowledgment">承认</h4> <p>这项工作的部分资金支持科研补助金的17300036和17300036号从教育部、科学、文化、日本。</p></d我v><d我vclass="xml-content"> <h4 class="references" id="references">引用</h4> <ol> <li id="B1">c·凯利斯r·巴伯m . Flickner et al .,“高效和有效的查询图像内容,”<我>智能信息系统杂志》上</我>,3卷,不。3 - 4、231 - 262年,1994页。<年代p一个nclass="reflinks">视图:<一个href="https://doi.org/10.1007/BF00962238">出版商的网站</一个><年代p一个nclass="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=Efficient%20and%20effective%20querying%20by%20image%20content&author=C. Faloutsos&author=R. Barber&author=M. Flickner et al.&publication_year=1994" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B2">y Rubner和c .预<我>知觉指标为图像数据库导航</我>多德雷赫特,Kluwer学术出版商,Ntherlands, 2001。<年代p一个nclass="reflinks"></span></li> <li id="B3">美国Tsuge m . Shishibori y吴建,k .北城,“类似的音乐检索query-by-humming使用挖土机的距离,“<我>日本信息处理社会事务</我>,48卷,不。1,第311 - 300页,2007。<年代p一个nclass="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Similar%20music%20retrieval%20for%20the%20query-by-humming%20using%20the%20Earth%20Mover’s%20distance&author=M. Shishibori&author=Y. Ohnishi&author=S. Tsuge&author=&author=K. Kita&publication_year=2007" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B4">科恩和l . Guibas“挖土机的距离:下界和不变性在翻译,“技术。众议员cs - tr - 97 - 1597,斯坦福大学,1997年。<年代p一个nclass="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=The%20Earth%20Mover’s%20distance:%20lower%20bounds%20and%20invariance%20under%20translation&author=S. Cohen &author=L. Guibas&publication_year=1997" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B5">我同意,a .温家宝,t . Seidl”近似技术在多媒体数据库索引挖土机的距离,”<我>22日数据工程国际会议的程序(ICDE 06年)</我>p。11日,美国,2006年4月。<年代p一个nclass="reflinks">视图:<一个href="https://doi.org/10.1109/ICDE.2006.25">出版商的网站</一个><年代p一个nclass="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=Approximation%20techniques%20for%20indexing%20the%20earth%20mover's%20distance%20in%20multimedia%20databases&author=I. Assent&author=A. Wenning&author=&author=T. Seidl" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B6">w·Niblack r .理发师,w . Equitz et al .,“QBIC项目:查询图像的内容,使用的颜色,纹理,形状,”<我>为图片和视频数据库存储和检索</我>卷,1908<我>学报学报</我>圣何塞,页173 - 187年,加州,美国,1993年2月。<年代p一个nclass="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=QBIC%20project:%20querying%20images%20by%20content,%20using%20color,%20texture,%20and%20shape&author=W. Niblack&author=R. Barber&author=W. Equitz et al." target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B7">m·a·斯特里克和m . Orengo“彩色图像相似,”<我>存储和检索的图像和视频数据库三世</我>卷,2420<我>学报学报</我>圣何塞,页381 - 392年,加州,美国,1995年2月。<年代p一个nclass="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Similarity%20of%20color%20images&author=M. A. Stricker &author=M. Orengo" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B8">s . Ajiok s Tsuge m . Shishibori, k .北城,“快速多维最近邻搜索算法使用优先队列,“<我>我EEJ交易电子、信息和系统</我>,卷126,不。3、353 - 360年,2006页。<年代p一个nclass="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Fast%20multidimensional%20nearest%20neighbor%20search%20algorithm%20using%20priority%20queue&author=S. Ajiok&author=S. Tsuge&author=M. Shishibori&author=&author=K. Kita&publication_year=2006" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B9">o·贝利·m·沃曼,“快速、健壮的挖土机的距离”<我>学报》第12届国际会议上计算机视觉(ICCV ' 09)</我>2009年10月,页460 - 467。<年代p一个nclass="reflinks">视图:<一个href="https://doi.org/10.1109/ICCV.2009.5459199">出版商的网站</一个><年代p一个nclass="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=Fast%20and%20robust%20earth%20mover's%20distances&author=O. Pele &author=M. Werman" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B10">h .凌和k·冈田克也”,一个高效的挖土机的距离算法健壮的直方图比较,”<我>我EEE模式分析与机器智能</我>卷,29号5,840 - 853年,2007页。<年代p一个nclass="reflinks">视图:<一个href="https://doi.org/10.1109/TPAMI.2007.1058">出版商的网站</一个><年代p一个nclass="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=An%20efficient%20earth%20mover's%20distance%20algorithm%20for%20robust%20histogram%20comparison&author=H. Ling &author=K. Okada&publication_year=2007" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B11">p . n . Yianilos”数据结构和算法的最近邻搜索一般度量空间”<我>第四年度ACM-SIAM学报》研讨会上离散算法</我>1993年1月,页311 - 321。<年代p一个nclass="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Data%20structures%20and%20algorithms%20for%20nearest%20neighbor%20search%20in%20general%20metric%20spaces&author=P. N. Yianilos" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B12">p .彼得,m .髌骨和p .泽兹拉”M-tree:一个有效的访问在度量空间相似性搜索方法,”<我>诉讼的ACM SIGMOD国际会议管理的数据</我>,第79 - 71页,1995年。<年代p一个nclass="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=M-tree:%20an%20efficient%20access%20method%20for%20similarity%20search%20in%20metric%20spaces&author=P. Ciaccia&author=M. Patella&author=&author=P. Zezula" target="_blank">谷歌学术搜索</一个></年代p一个n></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</h4> <p>版权©2011 Masami Shishibori et al。这是一个开放的分布式下文章<一个rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</p></d我v></d我v></article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 becpDt hrTitleRef">更多相关文章</h4> <div id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 hFGNjP"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-cBdUnI hRnXob article_top_toolbar"> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-exkUMo hymroZ pdf_desktop 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src="data:image/svg+xml;base64,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" height="24"><span class="text">下载引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-BngTV hmDWcT ref_desktop" href="//www.newsama.com/journals/am/2011/421820.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-cTjmhe ihmyEq article_bottom_toolbar"> <div class="sc-cugefK itFKcQ accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="sc-dRFtgE jrsDZP">下载其他格式</年代p一个n><年代p一个nclass="sc-gkFcWv gWTCXQ">更多的</年代p一个n></年代p一个n> <span class="sc-htoDjs bMdQcY sc-gbOuXE jGPvPL icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-fnwBNb etzuBr"> <a class="sc-htpNat bUhGXt link sc-iNhVCk gWgCNb open_panel" href="//www.newsama.com/downloads/journals/am/2011/421820.xml" aria-label="XML" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> XML</d我v><我米g alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" 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height="24"><span class="sc-dRFtgE jrsDZP">订单打印副本</年代p一个n><年代p一个nclass="sc-gkFcWv gWTCXQ">订单</年代p一个n></年代p一个n><span class="sc-htoDjs kNoiZu sc-gbOuXE jGPvPL right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-hBbWxd kdRRST"> <div class="sc-dyGzUR cHatnS"> <div> 的观点<年代p一个n>3672年年</年代p一个n></d我v><d我v> 下载<年代p一个n>1552年年</年代p一个n></d我v></d我v> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2011/421820" data-style="small_circle"></span>引用</d我v></d我v></d我v><nav class="sc-bRBYWo fXBKFa sc-hUfwpO jHPgUP" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享文章</h3> <ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2011/421820&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" role="presentation" 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