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.expand_btn{-webkit-flex:1;-ms-flex:1;flex:1;background:url('data:image/svg+xml;base64,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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 .caption-partial-url{-webkit-flex:1;-ms-flex:1;flex:1;background:url('data:image/svg+xml;base64,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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 18px 19px 21px;}} .gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .gvEcCq .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .gvEcCq ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .gvEcCq ol li{margin:10px 0;padding-left:10px;word-break:normal;} .gvEcCq ol li a{word-break:break-all;} .gvEcCq ol li .reflinks{display:block;} .gvEcCq ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .gvEcCq ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .gvEcCq ol li .reflinks .sep{color:#000000;} .gvEcCq .table-wrapper{width:auto;overflow-x:auto;} .gvEcCq .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .gvEcCq .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 1px rgba(255,255,255,.5);} @media (min-width:768px){.gvEcCq .table-wrapper{overflow-x:auto;width:auto;-webkit-break-word:word-break;break-word:word-break;margin:0 auto;}} @media (min-width:992px){.gvEcCq .table-wrapper{width:auto;}} @media (min-width:1324px){.gvEcCq .table-wrapper{width:auto;}} @media (min-width:320px){.gvEcCq{margin-bottom:33px;padding:0;}} @media (min-width:992px){.gvEcCq{padding:0;margin-bottom:100px;}} @media (min-width:1325px){.gvEcCq{margin-bottom:100px;}} .gvEcCq .owl-stage{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .gvEcCq .floats-partial-middle--thumbs{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .gvEcCq .floats-partial-middle--thumbs .partial-carousel-dot svg{fill:#4D8A17;} .gvEcCq .floats-partial-middle--thumbs .partial-carousel-dot strong{color:#4D8A17;font-weight:500;} .gvEcCq .floats-partial-middle--thumbs .partial-carousel-dot.active strong{color:#007B8B;} .gvEcCq .floats-partial-middle--thumbs .partial-carousel-dot.active svg{fill:#007B8B;} .gvEcCq .floats-partial-middle--thumbs .partial-carousel-dot .nowrap{white-space:nowrap;} .gvEcCq .partial-carousel-dot{text-align:center;cursor:pointer;border:0;width:100px;padding-bottom:20px;background-color:#fff;display:table-cell;} .gvEcCq .partial-carousel-dot:focus-visible{outline-offset:-3px;} .gvEcCq .partial-carousel-dot strong{font-size:11px;padding-top:12px;} @media (min-width:767.5px){.gvEcCq .partial-carousel-dot strong{font-size:16px;}} .gvEcCq .partial-carousel-dot img{width:90px;height:90px;border:1px solid #979797;margin:10px 0;} .gvEcCq .partial-carousel-wrapper .floats-partial-middle{border-top:1px solid #e3e3e3;display:block;margin-bottom:50px;padding-top:1px;} @media (min-width:767.5px){.gvEcCq .partial-carousel-wrapper .floats-partial-middle{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;margin-bottom:0;}} .gvEcCq .partial-carousel--single-image{overflow:hidden;text-align:center;} .gvEcCq .partial-carousel--single-image img{width:100%;max-height:239px;height:auto;} @media (min-width:767.5px){.gvEcCq .partial-carousel--single-image img{max-height:357px;}} @media (min-width:991.5px){.gvEcCq .partial-carousel--single-image img{max-height:417px;}} .gvEcCq .partial-carousel--single-image strong{font-size:11px;padding-top:12px;} @media (min-width:767.5px){.gvEcCq .partial-carousel--single-image strong{font-size:16px;}} .gvEcCq .owl-nav,.gvEcCq .owl-dots{display:none;} .gvEcCq .partial-carousel-wrapper .owl-loaded{position:relative;height:auto;max-height:287px;} @media (min-width:767.6px){.gvEcCq .partial-carousel-wrapper .owl-loaded{max-height:414px;}} @media (min-width:767.5px){.gvEcCq .partial-carousel-wrapper .owl-loaded{max-height:477px;}} .gvEcCq .partial-carousel-wrapper .floats-partial-content,.gvEcCq .owl-stage-outer,.gvEcCq .owl-stage{max-height:287px;height:auto;} @media 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href="//www.newsama.com/journals/cin/" aria-label="Computational Intelligence and Neuroscience">计算智能和神经科学</一个>/<一个class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/cin/contents/year/2011/" aria-label="2011">2011年</一个>/<年代pan class="sc-bhlBdH UVThf">文章</年代pan> </div> <div class="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> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD 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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"> <div class="sc-kxynE fgGykB"> <span class="sc-cooIXK gQxyld">特殊的问题</年代pan> <h2 class="sc-fcdeBU bVtmCk">选择从第四届国际会议论文Bioinspired系统信号处理和认知</h2><一个class="sc-htpNat bUhGXt link sc-gmeYpB hSHJbi" href="//www.newsama.com/journals/cin/si/106351/" aria-label="">把这个特殊的问题</一个><hrclass="sc-clNaTc ktFfKO"> </div> <p class="sc-kZmsYB bkiEfx article_type">研究文章|开放获取</p> <div class="sc-RcBXQ ztvYg article_citation"> 体积 2011年 <span class="sc-fZwumE cUsFHx">|</年代pan>文章的ID 217987年 <span class="sc-fZwumE cUsFHx">|</年代pan> <a class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2011/217987" aria-label="Doi-link">https://doi.org/10.1155/2011/217987</一个></div> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>迪特尔•Devlaminck巴特wyn,莫里茨Grosse-Wentrup,乔治•Otte帕特里克Santens, ”<年代pan class="adjust-article-svg-size">综合性学习Motor-Imagery BCI的常见的空间模式</年代pan>”,<i>计算智能和神经科学</我>, 卷。2011年, 文章的ID217987年, 9   页面, 2011年。 https://doi.org/10.1155/2011/217987</p> </div> <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">综合性学习Motor-Imagery BCI的常见的空间模式</h1></div> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class=""><b>迪特尔Devlaminck</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></span> <span class="">巴特温,<年代up>1</年代up></span> <span class="">莫里茨Grosse-Wentrup,<年代up>2</年代up></span> <span class="">乔治Otte,<年代up>3</年代up> 和</年代pan> <span class="">帕特里克Santens<年代up>4</年代up></span> <div class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</年代up><span>电能、系统和自动化,根特大学913年Technologiepark Zwijnaarde, 9052绅士,比利时</年代pan></p> <p><sup>2</年代up><span>部门的经验推断,马克斯普朗克生物控制论,Spemannstr。38, 72076图宾根,德国</年代pan></p> <p><sup>3</年代up><span>pc Guislain博士Fr。Ferrerlaan 88 a, 9000绅士,比利时</年代pan></p> <p><sup>4</年代up><span>De Pintelaan神经学部门,根特大学医院,185年,9000年的绅士,比利时</年代pan></p> </div> <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>法比奥Babiloni</div> <div class="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pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年3月14日</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">修改后的</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年7月28日</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年7月29日</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年10月11日</年代pan> </div> </div> </div> <article class="sc-jtRlXQ gvEcCq article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4><p>Motor-imagery-based脑-机接口(bci)通常使用常见的空间模式过滤器(CSP)之前的预处理步骤特征提取和分类。监督算法CSP方法,因此需要科目的训练数据校准,这是非常耗时的收集。为了减少校准数据,需要一个新的主题,一个可以应用多任务(从现在开始称为综合性)机器学习技术的预处理阶段。在这里,综合性学习的目的是学习一个新的主题空间滤波器基于自己的数据和其他科目。本文概述了多任务的细节CSP算法和显示结果在两个数据集。在某些科目可以看到明显改善,特别是当训练试验的数量相对较低。</p> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4><p>BCI系统的开发是一个活跃的研究领域,目标来帮助人们,患有严重残疾,恢复通信环境通过另一个接口。这样的BCI系统可分为几类基于他们所使用的信号特征。其中的一些特性,比如P300 [<一个href=”#B1">1</一个>)和稳态视觉诱发电位(ssvep) [<一个href=”#B2">2</一个>)是由外界刺激引起自然而其他像感觉运动节奏死因特异性)可以独立调节的问题。的,这可以通过执行任务的想象不同的动作,如左、右手运动,或脚和舌头的运动。皮质参与运动机能(和运动图像)显示出强劲的8 - 12赫兹(甚至18-26 Hz)活动当人不执行任何电动机(图像)的任务。然而,当人从事电动机任务时,神经网络在相应的大脑皮层区域被激活。这一块空闲同步放电的神经元,从而导致可衡量的衰减频带。减少权力也被称为事件相关去同步化(ERD) [<一个href=”#B3">3</一个>],相反的效果称为与事件相关同步(人)。的位置(电极)这一特性取决于电机的类型的任务。举个例子,如果一个人他的左臂移动,运动的大脑区域侧(电极周围C4)将显示ERD特性,在神经元的细胞内电位侧皮质运动区继续振荡更加同步。</p> <p>由于低空间分辨率的脑电图(EEG),一个常用的方法来改善这一决议是常见的空间模式(CSP)算法引入的kol [<一个href=”#B4">4</一个>)检测异常脑电图活动。之后,它被用于歧视想象手运动的任务(<一个href=”#B5">5</一个>,<一个href=”#B6">6</一个>]。从那时起,很多组织改进CSP的基本算法与时间过滤(通过扩展<一个href=”#B7">7</一个>对非平稳[],使它更健壮<一个href=”#B8">8</一个>)或减少上一次校准时间转移知识学习(<一个href=”#B9">9</一个>]。十多年后,这种方法仍然证明了其优越性从第四(BCI竞争的结果<一个href=”http://www.bbci.de/competition/iv/" target="_blank">http://www.bbci.de/competition/iv/</一个>你可以找到的数据集和结果第四BCI竞争)。不过,这比P300-based BCI BCI设置不准确,首先需要一个较长的训练时间。一些人甚至无法实现适当的控制。</p> <p>进一步提高科目的CSP滤波器的一种方法是使用来自其他学科的数据记录,另外主题的数据。为此,我们将使用一些想法的综合性学习,机器学习的一个活跃的话题(<一个href=”#B10">10</一个>,<一个href=”#B11">11</一个>]。在[<一个href=”#B12">12</一个>),作者运用这一概念学习分类器,能够从多个学科,导致一个算法执行新的科目即使没有培训。分类器可以适应新数据变得可用时,与训练样本很少达成更高的分类精度。然而,他们应用拉普拉斯算子的过滤器,而不是基于CSP的空间滤波器算法和使用特性从脑电图信号获得滤波后在不同的传输频带。与他们的方法,我们将从基本算法CSP和综合性学习的概念应用于预处理阶段。一般来说,综合性学习算法假设所有任务相似。在我们的第一个方法中,我们也会假定所有科目也有类似的头部模型,因此,空间过滤器可以分解成一个科目的一部分和一个全球的部分。在第二个方法中,我们不会做这样的假设,而是我们假定他们被组合在一起在一个固定数量的集群。此外,我们包括参数之间做出权衡这些全球和科目的过滤器。</p> <p>部分<一个href=”#sec2">2</一个>给了第一种方法的细节我们的综合性CSP算法,而部分<一个href=”#sec4">4</一个>介绍了基于集群的综合性CSP算法。部分<一个href=”#sec3">3</一个>提出了一种优化聚类框架CSP过滤器,这也将在后续部分中使用<一个href=”#sec4">4</一个>。结果与基本算法CSP部分<一个href=”#sec5">5</一个>在一个模拟数据集和两个实验数据集,其中一个是公开在网站上第三BCI竞争(<一个href=”#B13">13</一个>14)和一个包含数据对象记录马克斯普朗克研究所的生物控制论。部分<一个href=”#sec6">6</一个>该方法的优点和缺点。</p> <h4 id="multisubject-csp-formulation-as-a-sum-of-convex-to-convex-ratios">2。综合性CSP配方的总和Convex-to-Convex比率</h4><p>基本CSP方法的目标是学习的一组为一个主题空间过滤器最大化信号方差试验的一个类,同时最小化信号方差为试验的其他类。在两种情况下,这可以制定如下:<年代pan class="equation" id="EEq1"> <svg height="36.400002" id="M1" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 36.400002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,36.4)"> <g transform="translate(72,-42.88)"> <text transform="matrix(1,0,0,-1,171.13,53.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代pan> </text> <text transform="matrix(1,0,0,-1,179.78,46.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,198.03,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.05,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.77,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,221.57,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,232.27,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 198.03,56.91 43.27,0" 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,-1,198.03,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.05,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.77,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,221.57,48.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,232.27,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-10.67"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="241.85001" y="-10.67"> (</t年代pan> <tspan style="font-size: 12.50px; " x="246.0135" y="-10.67"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="252.265" y="-10.67"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="13.775" id="M2" style="vertical-align:-0.0pt;width:23.25px;" version="1.1" viewbox="0 0 23.25 13.775" width="23.25" 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"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.15,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.775" id="M3" style="vertical-align:-0.0pt;width:23.25px;" version="1.1" viewbox="0 0 23.25 13.775" width="23.25" 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"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.15,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> </g> </g> </svg>对应于试验的协方差矩阵对应于第一和第二课,分别。</p> <p>我们现在想要使用其他科目的数据提高过滤器的特定主题。为此,我们首先需要一个空间滤波器<年代vg height="11.3625" id="M4" style="vertical-align:-3.2316pt;width:16.85px;" version="1.1" viewbox="0 0 16.85 11.3625" width="16.85" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>对于每一个主题,我们分解为一个全球性的和科目的一部分,<年代pan class="equation" id="eq1"> <svg height="15.75" id="M5" 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,-1,173.06,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,182.08,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,189.91,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,210.97,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,218.62,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.22,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,240.57,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="233.55" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="237.7135" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="243.965" y="0"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="17.75" id="M6" style="vertical-align:-3.25793pt;width:55.662498px;" version="1.1" viewbox="0 0 55.662498 17.75" width="55.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.58,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> ℝ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.2,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>代表了全球空间滤波器和学习所有科目和共享<年代vg height="17.7125" id="M7" style="vertical-align:-3.2316pt;width:51.537498px;" version="1.1" viewbox="0 0 51.537498 17.7125" width="51.537498" 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pan> </text> <text transform="matrix(1,0,0,-1,-65.7,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.88,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> ℝ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.5,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>代表了科目的过滤器的一部分。通道的数量是由<年代vg height="10.75" id="M8" 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pan> </text> </g> </g> </svg>。一个优化框架提出了我们学习这两种类型的过滤器。这可以作为制定<年代pan class="equation" id="EEq2"> <svg height="50.837502" id="M9" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.837502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.8375)"> <g transform="translate(72,-31.33)"> <text transform="matrix(1,0,0,-1,100.75,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代pan> </text> <text transform="matrix(1,0,0,-1,104.76,40.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,111.08,37.87)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,114.71,40.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,121.27,37.87)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,135.54,63.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,130.62,41.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,131.58,33.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.01,56.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,215.04,61.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.75,56.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,229.55,62.97)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,240.26,56.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,249.28,53.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 147.96,50.81 163.72,0" 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,-1,147.96,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,156.99,40.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="7.1599998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,163.7,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,171.51,42.01)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,182.21,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,191.24,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,198.36,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.47,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,221.35,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="6.5300002" y="0.49000001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.91,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,241.79,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> </text> <text transform="matrix(1,0,0,-1,250.41,41.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,258.06,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,276.17,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,281.04,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="6.54" y="0.49000001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,293.83,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,298.18,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> </text> <text transform="matrix(1,0,0,-1,306.81,41.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,312.88,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="161.24001" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="165.4035" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="171.655" y="0"> )</t年代pan> </text> </g> </g> </svg></span>哪里用的<年代vg height="10.725" id="M10" style="vertical-align:-0.1254pt;width:11.375px;" version="1.1" viewbox="0 0 11.375 10.725" width="11.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。</p> <p>的参数<年代vg height="14.475" id="M11" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.475" id="M12" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>使我们之间做出权衡全球或特定的过滤器。高的价值<年代vg height="14.475" id="M13" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和低的价值<年代vg height="14.475" id="M14" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>,向量<年代vg height="11.3875" id="M15" style="vertical-align:-3.25793pt;width:17.5px;" version="1.1" viewbox="0 0 17.5 11.3875" width="17.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3875)"> <g transform="translate(72,-62.89)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>被迫零和一个特定的过滤器。当<年代vg height="14.475" id="M16" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>高,<年代vg height="14.475" id="M17" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>低,向量<年代vg height="11.3625" id="M18" style="vertical-align:-3.2316pt;width:13.375px;" version="1.1" viewbox="0 0 13.375 11.3625" width="13.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>被迫0和更多的全球过滤器计算。此外,还可以执行一个正则化选择<年代vg height="14.475" id="M19" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.475" id="M20" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>高。</p> <p>上述方程可以改写一个更简单的形式,也就是说,一笔convex-to-convex比率<年代pan class="equation" id="EEq3"> <svg height="53" id="M21" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 53" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,53)"> <g transform="translate(72,-29.6)"> <text transform="matrix(1,0,0,-1,88.71,47.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代pan> </text> <text transform="matrix(1,0,0,-1,97.36,40.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,114.41,47.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="15.491217" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.518383" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="29.732134" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.496258" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="44.13559" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="56.163475" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="65.890808" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="71.442139" y="0"> x</t年代pan> </text> <text transform="matrix(1,0,0,-1,179.23,40.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="21.98" y="-23.57"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,196.28,41.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,197.25,33.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,212.44,47.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,217.54,44.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225.36,47.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="27.306553" y="0"> x</t年代pan> </text> <text transform="matrix(1,0,0,-1,246.05,40.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="21.969999" y="-23.57"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,263.1,41.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,264.06,33.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,280.45,56.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.47,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 296.19,68.08 7.8,0" 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,-1,296.19,56.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,303.99,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="12.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,314.69,56.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 280.45,50.8 43.27,0" 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,-1,280.45,32.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.47,36.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 296.19,44.04 7.8,0" 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,-1,296.19,32.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,303.99,42)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,314.69,32.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-14.8"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="159.42999" y="-14.8"> (</t年代pan> <tspan style="font-size: 12.50px; " x="163.59351" y="-14.8"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="169.845" y="-14.8"> )</t年代pan> </text> </g> </g> </svg></span>与<年代pan class="equation" id="eq2"> <svg height="415.71249" id="M22" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 415.71249" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,415.7125)"> <g transform="translate(72,260.57)"> <text transform="matrix(1,0,0,-1,147.03,56.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,156.06,61.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,166.24,56.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.4" y="1.87"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,194.67,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,207.36,54.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.61,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,226.3,54.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋯</t年代pan> <tspan style="font-size: 12.50px; " x="19.629709" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.19,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.99,51.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6899996" y="-4.9200001"> ,</t年代pan> </text> <g> <path d="m 166.76,34.11 7.8,0" 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,-1,166.76,22.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,174.56,32.06)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,188.74,22.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,209.7,19.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,214.05,22.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,221.86,28.99)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,232.56,22.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,242.24,27.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="8.1300001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,248.95,22.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> </text> <g> <path d="m 126.51,6.35 7.8,0" 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,-1,126.51,-4.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,134.31,4.31)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,148.49,-4.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,169.46,-7.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.8,-4.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,181.61,1.24)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,192.31,-4.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,201.99,0.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="8.1300001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,211.48,-4.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,229.58,-7.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,234.46,-4.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.34,-7.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,251.99,-4.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,270.1,-7.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,274.97,-4.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,284.85,-7.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.2,-4.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-124.18" y="65.860001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.94,-73.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,181.77,-70.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="-38.080002"> ⎛</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="-26.290001"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="-14.5"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="-2.71"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="9.0799999"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="20.879999"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="32.669998"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="44.400002"> ⎝</t年代pan> <tspan style="font-size: 12.50px; " x="28.469999" y="-35.630001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.24,-38.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,200.09,-60.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.34,-63.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.765296" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="12.760416" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="17.136415" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="20.050833" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="24.706896" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="30.308176" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,210.24,-85.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.24,-88.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,199.43,-110.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,205.68,-113.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="8.6032162" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="14.598336" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="18.449217" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="21.363632" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="26.019695" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="31.620975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,242.98,-32.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎞</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="11.79"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="23.58"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="35.369999"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="47.16"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="58.959999"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="70.75"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="82.480003"> ⎠</t年代pan> <tspan style="font-size: 12.50px; " x="7.71" y="38.080002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-107.29" y="122.07"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,145.57,-157.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,153.92,-154.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-13.09"> ⎛</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-2.24"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="8.6099997"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="19.389999"> ⎝</t年代pan> <tspan style="font-size: 12.50px; " x="20.629999" y="-10.63"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.55,-147.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.58,-169.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,177.84,-172.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="5.6887999" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="15.946144" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,199.46,-141.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎞</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.85"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="21.700001"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="32.48"> ⎠</t年代pan> <tspan style="font-size: 12.50px; " x="7.71" y="18.01"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.08" y="14.96"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,220.54,-159.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,242.45,-156.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,248.7,-159.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="15.946144" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,270.33,-159.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6800003" y="-4.9200001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-168.41" y="66.559998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,111.8,-229.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,119.62,-226.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-25.58"> ⎛</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-14.08"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-2.5699999"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="8.9399996"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="20.450001"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="31.889999"> ⎝</t年代pan> <tspan style="font-size: 12.50px; " x="26.42" y="-23.129999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,152.29,-206.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="8.5069437" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="14.108224" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,148.09,-228.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,154.09,-231.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,137.28,-253.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,143.54,-256.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="8.6032162" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="14.598336" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="18.449217" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="21.363632" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="26.019695" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="31.620975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.84,-200.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎞</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="11.5"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="23.01"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="34.52"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="46.029999"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="57.470001"> ⎠</t年代pan> <tspan style="font-size: 12.50px; " x="7.71" y="28.09"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.56" y="25.58"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,200.65,-229.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="14.108224" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,230.4,-226.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.4,-229.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,262.3,-226.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,268.55,-229.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="13.17176" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="18.860559" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="24.85568" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="28.70656" y="0"> )</t年代pan> <tspan style="font-size: 8.75px; " x="31.620975" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,305.85,-228.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="168.27" y="-131.24001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="172.4335" y="-131.24001"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="178.685" y="-131.24001"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.5125" id="M23" style="vertical-align:-3.35449pt;width:27.549999px;" version="1.1" viewbox="0 0 27.549999 14.5125" width="27.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5125)"> <g transform="translate(72,-60.39)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.95,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.656064" y="0"> ×</t年代pan> <tspan style="font-size: 8.75px; " x="10.257344" y="0"> </t年代pan> </text> </g> </g> </svg>代表了<年代vg height="10.75" id="M24" 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pan> </text> </g> </g> </svg>维统一矩阵。</p> <p>找到最大的(<一个href=”#EEq3">4</一个>我们用牛顿法。为此,我们需要梯度和黑森(<一个href=”#EEq3">4</一个>)。的梯度,<年代pan class="equation" id="eq3"> <svg height="53" id="M25" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 53" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,53)"> <g transform="translate(72,-29.6)"> <text transform="matrix(1,0,0,-1,108.27,47.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∇</t年代pan> </text> <text transform="matrix(1,0,0,-1,117.41,44.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,124.23,47.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="15.491217" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.518383" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="29.732134" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.496258" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="44.123089" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="56.163475" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,191.58,63.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,186.65,41.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,187.62,33.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代pan> </text> <g> <path d="m 204,68.08 7.8,0" 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,-1,204,56.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,211.8,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="12.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,222.51,56.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,250.76,53.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,257.19,56.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> )</t年代pan> </text> <g> <path d="m 276.63,68.08 7.8,0" 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,-1,276.63,56.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,284.43,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="12.24"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,295.13,56.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 204,50.8 100.16,0" 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,-1,232.45,32.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,241.47,36.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 248.19,44.04 7.8,0" 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,-1,248.19,32.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,255.99,42)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,266.69,32.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="38.669998" y="-14.8"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="207.42999" y="-14.8"> (</t年代pan> <tspan style="font-size: 12.50px; " x="211.59351" y="-14.8"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="217.845" y="-14.8"> )</t年代pan> </text> </g> </g> </svg></span>海赛是由,<年代pan class="equation" id="eq4"> <svg height="198.6875" id="M26" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 198.6875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,198.6875)"> <g transform="translate(72,86.95)"> <text transform="matrix(1,0,0,-1,88.45,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∇</t年代pan> </text> <text transform="matrix(1,0,0,-1,97.59,44.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,106.49,45.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.52"> ∇</t年代pan> </text> <text transform="matrix(1,0,0,-1,121.49,44.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,128.3,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2600002" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.58" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.607885" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,170.1,63.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,165.17,41.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,166.14,33.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,165.42,7.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎡</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="11.73"> ⎢</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="23.450001"> ⎢</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="35.119999"> ⎣</t年代pan> <tspan style="font-size: 12.50px; " x="6.8200002" y="4.9000001"> </t年代pan> </text> <g> <path d="m 179.6,18.55 7.8,0" 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,-1,179.6,7.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,187.4,16.5)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,200.89,7.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,217.33,4.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 221.68,18.55 7.8,0" 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,-1,221.68,7.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,229.48,16.5)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,242.96,7.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> ∇</t年代pan> </text> <text transform="matrix(1,0,0,-1,263.45,13.43)"> <tspan style="font-size: 8.75px; " x="0" y="8.8800001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.765296" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,273.62,7.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,282.65,12.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 289.36,18.55 7.81,0" 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,-1,289.36,7.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,297.17,16.5)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,307.87,2.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 172.24,-3.92 143.23,0" 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,-1,238.54,-15.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.82,-18.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,176.57,-66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="9.7600002" y="-9.5100002"> </t年代pan> </text> <g> <path d="m 193.7,-40.6 7.8,0" 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,-1,193.7,-51.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,201.5,-42.64)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,212.2,-51.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,240.45,-54.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 244.8,-40.6 7.81,0" 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,-1,244.8,-51.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,252.61,-42.64)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,263.31,-51.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.0299997" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.709999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,291.05,-46.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 297.76,-40.6 7.8,0" 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,-1,297.76,-51.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,305.56,-42.64)"> <tspan style="font-size: 8.75px; " x="0" y="12.25"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <g> <path d="m 186.33,-63.06 129.94,0" 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,-1,245.72,-76.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.01,-71.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.1999998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,317.46,-51.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎤</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="11.73"> ⎥</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="23.459999"> ⎥</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="35.119999"> ⎦</t年代pan> <tspan style="font-size: 12.50px; " x="7.71" y="14.41"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="156.66" y="-41.18"> (</t年代pan> <tspan style="font-size: 12.50px; " x="160.8235" y="-41.18"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="167.075" y="-41.18"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.5875" id="M27" style="vertical-align:-3.2316pt;width:13.425px;" version="1.1" viewbox="0 0 13.425 14.5875" width="13.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.66,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>短暂的分母项<年代vg height="11.05" id="M28" style="vertical-align:-3.2316pt;width:11.9375px;" version="1.1" viewbox="0 0 11.9375 11.05" width="11.9375" 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pan> </text> <text transform="matrix(1,0,0,-1,-66.85,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="18.775" id="M29" style="vertical-align:-2.96555pt;width:24.275px;" version="1.1" viewbox="0 0 24.275 18.775" width="24.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.775)"> <g transform="translate(72,-56.98)"> <text transform="matrix(1,0,0,-1,-71.95,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∇</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.81,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.8800001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="6.765296" y="0"> )</t年代pan> </text> </g> </g> </svg>的梯度<年代vg height="11.05" id="M30" style="vertical-align:-3.2316pt;width:11.9375px;" version="1.1" viewbox="0 0 11.9375 11.05" width="11.9375" 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pan> </text> <text transform="matrix(1,0,0,-1,-66.85,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>关于<年代vg height="7.5500002" id="M31" style="vertical-align:-0.17555pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 7.5500002" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.55)"> <g transform="translate(72,-65.96)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。</p> <p>从现在起,这个方法用缩写“mtCSP。”</p> <h4 id="an-optimization-framework-for-clustering-spatial-filters">3所示。聚类空间滤波器的优化框架</h4><p>之前的细节基于集群的综合性CSP算法,我们提出了一个聚类优化算法CSP过滤器。这个算法是受[<一个href=”#B14">14</一个>),将形成的基础在下一节中描述的算法。它还将用来找到一个好的初始化的变量基于集群的综合性CSP算法。</p> <p>所以,让我们开始提出了优化框架的简化版本(<一个href=”#B14">14</一个>]<年代pan class="equation" id="EEq4"> <svg height="50.837502" id="M32" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.837502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.8375)"> <g transform="translate(72,-31.33)"> <text transform="matrix(1,0,0,-1,145.68,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,144.84,40.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,149.78,38)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 6.25px; " x="2.75088" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,156.41,40.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,164.17,38)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,172.45,63.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.06,41.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.57,33.96)"> <tspan style="font-size: 8.75px; " x="20.57" y="-29.67"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,184.21,41.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,185.18,33.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,200.36,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.42,44.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.51,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.4799995" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.34" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,239.8,44.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,245.04,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,256.5,44.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,260.85,45.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.52"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="213.27" y="-2.52"> (</t年代pan> <tspan style="font-size: 12.50px; " x="217.4335" y="-2.52"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="223.685" y="-2.52"> )</t年代pan> </text> </g> </g> </svg></span><span class="equation" id="EEq5"> <svg height="50.662498" id="M33" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.662498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.6625)"> <g transform="translate(72,-31.47)"> <text transform="matrix(1,0,0,-1,134.45,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,141.5,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,154.06,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="14.115887" y="0"> {</t年代pan> <tspan style="font-size: 12.50px; " x="20.117327" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="26.368828" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.582579" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.83408" y="0"> }</t年代pan> <tspan style="font-size: 12.50px; " x="45.923519" y="0"> ,</t年代pan> </text> <text transform="matrix(1,0,0,-1,229.51,63.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225.12,41.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225.64,34.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,241.27,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,248.32,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,260.89,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="213.23" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="217.39349" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="223.645" y="0"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.325" id="M34" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" 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pan> </text> </g> </g> </svg>是集群的数量,<年代vg height="10.725" id="M35" style="vertical-align:-0.1254pt;width:11.375px;" version="1.1" viewbox="0 0 11.375 10.725" width="11.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>观察的数量,<年代vg height="11.3625" id="M36" style="vertical-align:-3.2316pt;width:13.375px;" version="1.1" viewbox="0 0 13.375 11.3625" width="13.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>的观察,<年代vg height="11.1875" id="M37" style="vertical-align:-3.2316pt;width:16.612499px;" version="1.1" viewbox="0 0 16.612499 11.1875" width="16.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1875)"> <g transform="translate(72,-63.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64,63.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>集群中心和<年代vg height="10.75" id="M38" 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pan> </text> </g> </g> </svg>一个距离函数。二进制系数<年代vg height="11.05" id="M39" style="vertical-align:-3.2316pt;width:20.299999px;" version="1.1" viewbox="0 0 20.299999 11.05" width="20.299999" 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pan> </text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>表明某个对象所属集群。这最小化通常骑自行车通过两个步骤来解决。在第一步中,系数<年代vg height="11.05" id="M40" style="vertical-align:-3.2316pt;width:20.299999px;" version="1.1" viewbox="0 0 20.299999 11.05" width="20.299999" 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pan> </text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>确定通过设置<年代vg height="10.7375" id="M41" 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pan> </text> </g> </g> </svg>如果该对象th系数<年代vg height="11.3625" id="M42" style="vertical-align:-3.2316pt;width:13.375px;" version="1.1" viewbox="0 0 13.375 11.3625" width="13.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是最接近集群中心<年代vg height="11.1875" id="M43" style="vertical-align:-3.2316pt;width:16.612499px;" version="1.1" viewbox="0 0 16.612499 11.1875" width="16.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1875)"> <g transform="translate(72,-63.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64,63.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg><span class="equation" id="eq5"> <svg height="56.862499" id="M44" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 56.862499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,56.8625)"> <g transform="translate(72,-26.51)"> <text transform="matrix(1,0,0,-1,109.89,46.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,116.94,43.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,129.5,46.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-12.07"> ⎧</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-6.9400001"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="3.1900001"> ⎨</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="13.31"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="18.379999"> ⎩</t年代pan> <tspan style="font-size: 12.50px; " x="63.220001" y="-12.49"> </t年代pan> <tspan style="font-size: 12.50px; " x="69.07" y="-15"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.040001" y="-15"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="26.2915" y="-15"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="41.92025" y="-15"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="45.396084" y="-15"> f</t年代pan> <tspan style="font-size: 12.50px; " x="53.723083" y="-15"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.52,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,211.76,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,223.22,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,227.57,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.85" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.700001" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> <</t年代pan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,272.22,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,275.68,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,287.14,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,291.49,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-90.18" y="12.55"> ∀</t年代pan> <tspan style="font-size: 12.50px; " x="-83.178322" y="12.55"> </t年代pan> <tspan style="font-size: 12.50px; " x="-75.739037" y="12.55"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="-61.610645" y="12.55"> {</t年代pan> <tspan style="font-size: 12.50px; " x="-55.609203" y="12.55"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="-49.357704" y="12.55"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-44.156456" y="12.55"> …</t年代pan> <tspan style="font-size: 12.50px; " x="-29.565456" y="12.55"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-24.351706" y="12.55"> </t年代pan> <tspan style="font-size: 12.50px; " x="-13.824179" y="12.55"> }</t年代pan> <tspan style="font-size: 12.50px; " x="-5.0470729" y="12.55"> ⧵</t年代pan> <tspan style="font-size: 12.50px; " x="4.267662" y="12.55"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.044288" y="12.55"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-141.95" y="27.549999"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-135.6985" y="27.549999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-120.06975" y="27.549999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="-113.90577" y="27.549999"> t</t年代pan> <tspan style="font-size: 12.50px; " x="-110.34241" y="27.549999"> h</t年代pan> <tspan style="font-size: 12.50px; " x="-104.09092" y="27.549999"> e</t年代pan> <tspan style="font-size: 12.50px; " x="-98.539581" y="27.549999"> r</t年代pan> <tspan style="font-size: 12.50px; " x="-94.138527" y="27.549999"> w</t年代pan> <tspan style="font-size: 12.50px; " x="-85.111359" y="27.549999"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="-81.635529" y="27.549999"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="-76.771858" y="27.549999"> e</t年代pan> <tspan style="font-size: 12.50px; " x="-71.220528" y="27.549999"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="176.38" y="12.49"> (</t年代pan> <tspan style="font-size: 12.50px; " x="180.5435" y="12.49"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="186.795" y="12.49"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="193.04649" y="12.49"> )</t年代pan> </text> </g> </g> </svg></span>在第二步中,我们发现集群中心最小化总距离他们的集群成员决定的系数<年代vg height="11.05" id="M45" style="vertical-align:-3.2316pt;width:20.299999px;" version="1.1" viewbox="0 0 20.299999 11.05" width="20.299999" 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pan> </text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>在上一步中计算。鉴于系数<年代vg height="11.05" id="M46" style="vertical-align:-3.2316pt;width:20.299999px;" version="1.1" viewbox="0 0 20.299999 11.05" width="20.299999" 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pan> </text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>,我们可以看到,内部资金是相互独立的,因此也可以相互独立地进行了优化。一个典型的距离函数是欧几里得距离。</p> <p>然而,对于空间过滤器,我们必须找到一个更合适的指标。在[解释<一个href=”#B9">9</一个>),不是欧几里得CSP的空间过滤器。改变长度或CSP过滤无关紧要的标志,因为它仍然是一个瑞利商的解决方案(<一个href=”#EEq1">1</一个>)。换句话说,过滤器都可以认为躺在单位超球面,因此我们采用一个angle-based度量。这个指标时应该零角度是零个或两个空间之间的过滤器<年代vg height="7.0124998" id="M47" style="vertical-align:-0.16302pt;width:9.625px;" version="1.1" viewbox="0 0 9.625 7.0124998" width="9.625" 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,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>左边的和最大的时候<年代vg height="10.9125" id="M48" style="vertical-align:-0.17555pt;width:21.7875px;" version="1.1" viewbox="0 0 21.7875 10.9125" width="21.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.5893211" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="11.065155" y="0"> 2</t年代pan> </text> </g> </g> </svg>组成。因此,角的正弦平方<年代vg height="10.7375" id="M49" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" 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pan> </text> </g> </g> </svg>这两个过滤器之间似乎是一个合适的指标<年代pan class="equation" id="eq6"> <svg height="80.150002" id="M50" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 80.150002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,80.15)"> <g transform="translate(72,-7.88)"> <text transform="matrix(1,0,0,-1,118.8,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.4899998" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.34" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,140.39,57.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,145.27,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,156.73,57.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,161.6,58.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.52"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.52"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="26.221554" y="-2.52"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="29.697388" y="-2.52"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,199.64,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.6,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.702568" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="18.341902" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.38229" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="39.409454" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="50.749676" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="56.30101" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="62.552509" y="0"> 年代</t年代pan> </text> <text transform="matrix(1,0,0,-1,276.11,65.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,283.07,60.78)"> <tspan style="font-size: 12.50px; " x="-62.040001" y="29.5"> </t年代pan> <tspan style="font-size: 12.50px; " x="-56.18" y="26.98"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.702568" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-112.14" y="37.560001"> =</t年代pan> <tspan style="font-size: 12.50px; " x="-100.11211" y="37.560001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="-91.084946" y="37.560001"> −</t年代pan> </text> <text transform="matrix(1,0,0,-1,233.14,38.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,239.85,33.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,246.1,30.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,250.98,31.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,256.83,41.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 204.53,26.34 73.67,0" 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,-1,204.53,10.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.64,17.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,223.35,12.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,229.6,9.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,234.47,10.13)"> <tspan style="font-size: 12.50px; " x="13.79" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9269018" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.51,17.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,261.22,12.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,267.48,9.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,272.35,10.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.0500002" y="-13.09"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="195.52" y="-26.68"> (</t年代pan> <tspan style="font-size: 12.50px; " x="199.6835" y="-26.68"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="205.935" y="-26.68"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="212.18649" y="-26.68"> )</t年代pan> </text> </g> </g> </svg></span>我们现在可以填补这个表达式(<一个href=”#EEq4">8</一个>)和不断下降的解决方案之一,因为它并没有改变优化问题。符号也可以下降如果我们变换(<一个href=”#EEq4">8</一个>)为最大化问题,导致,<年代pan class="equation" id="eq7"> <svg height="112.5875" id="M51" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 112.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,112.5875)"> <g transform="translate(72,18.07)"> <text transform="matrix(1,0,0,-1,131.09,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代pan> </text> <text transform="matrix(1,0,0,-1,130.92,40.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,135.85,37.87)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 6.25px; " x="2.75088" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,142.49,40.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,151,37.87)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,159.28,63.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,154.89,41.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,155.4,33.96)"> <tspan style="font-size: 8.75px; " x="20.57" y="-29.67"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,171.04,41.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,172.01,33.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,187.19,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,194.24,44.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.61,55.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,237.48,63.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.2,58.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,250.45,55.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.8,55.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,260.65,65.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 204.53,50.81 79.07,0" 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,-1,204.53,34.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.41,41.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.12,37.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,235.15,33.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,240.39,34.6)"> <tspan style="font-size: 12.50px; " x="13.79" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9269018" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,260.43,41.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="7.1599998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,267.14,37.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,273.4,33.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,277.74,34.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.0500002" y="-13.09"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-142.25" y="36.310001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,142.54,-4.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,155.11,-1.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="14.115887" y="0"> {</t年代pan> <tspan style="font-size: 12.50px; " x="20.117327" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="26.368828" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.570074" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.821575" y="0"> }</t年代pan> <tspan style="font-size: 12.50px; " x="45.911015" y="0"> ,</t年代pan> </text> <text transform="matrix(1,0,0,-1,230.55,14.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.16,-8.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.68,-15.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,242.32,-1.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,249.37,-4.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.93,-1.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="205.94" y="-25.549999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="210.1035" y="-25.549999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="216.355" y="-25.549999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="222.60651" y="-25.549999"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="11.3625" id="M52" style="vertical-align:-3.2316pt;width:17.9625px;" version="1.1" viewbox="0 0 17.9625 11.3625" width="17.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>代表了<年代vg height="10.7375" id="M53" 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pan> </text> </g> </g> </svg>集群中心。在算法的第二步,我们必须找到最优聚类中心<年代vg height="11.3625" id="M54" style="vertical-align:-3.2316pt;width:17.9625px;" version="1.1" viewbox="0 0 17.9625 11.3625" width="17.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>这可以独立完成每个集群(因此每个内心的总和)。在假设下<年代vg height="17.549999" id="M55" style="vertical-align:-3.2316pt;width:56.787498px;" version="1.1" viewbox="0 0 56.787498 17.549999" width="56.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.55)"> <g transform="translate(72,-57.96)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.99,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.73,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-44.91,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> </text> </g> </g> </svg>,这对集群内部和<年代vg height="10.7375" id="M56" 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pan> </text> </g> </g> </svg>可以写成<年代pan class="equation" id="EEq6"> <svg height="54.875" id="M57" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 54.875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,54.875)"> <g transform="translate(72,-28.1)"> <text transform="matrix(1,0,0,-1,153.74,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,162.77,62.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.57,52.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3600001" y="-4.9000001"> ∑</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.36,53.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> ∈</t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,205.89,51.4)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,212.36,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.61,54.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.96,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,229.21,62.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,235.93,52.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6800003" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.64,54.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 153.74,45.99 106.14,0" 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,-1,191.81,32.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,200.84,37.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.55,32.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.58,29.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.08,42.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="206.78999" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="210.95351" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="217.205" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="223.4565" y="0"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.5875" id="M58" style="vertical-align:-3.2316pt;width:16.8375px;" version="1.1" viewbox="0 0 16.8375 14.5875" width="16.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.82,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>所有过滤器,属于<年代vg height="10.7375" id="M59" 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pan> </text> </g> </g> </svg>集群。这个表达式必须最大化对<年代vg height="11.3625" id="M60" style="vertical-align:-3.2316pt;width:17.9625px;" version="1.1" viewbox="0 0 17.9625 11.3625" width="17.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>。最大的是协方差矩阵的主成分集群内的过滤器<年代vg height="10.7375" id="M61" 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pan> </text> </g> </g> </svg>因此等于最大特征值的特征向量对应的特征值分解。</p> <h4 id="cluster-based-multisubject-csp">4所示。基于集群的综合性CSP</h4><p>节<一个href=”#sec2">2</一个>,我们假设所有科目都相似。这种假设当然应该放松。在这里,我们提出一种算法,在集群组类似的主题。然后进行跨学科学习的每一个单独的集群。该方法受节中描述的优化算法<一个href=”#sec3">3</一个>。</p> <p>首先,我们引入多个共享过滤器<年代vg height="11.3625" id="M62" style="vertical-align:-3.2316pt;width:17.9625px;" version="1.1" viewbox="0 0 17.9625 11.3625" width="17.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,一个用于每个集群<年代vg height="10.7375" id="M63" 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pan> </text> </g> </g> </svg>,<年代pan class="equation" id="eq8"> <svg height="15.75" id="M64" 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,-1,168.13,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,177.16,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,189.72,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,210.79,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.81,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.4,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,245.5,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="222.37" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="226.53349" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="232.785" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="239.0365" y="0"> )</t年代pan> </text> </g> </g> </svg></span>我们现在可以变换问题(<一个href=”#EEq4">8</一个>)最大化问题和替换的距离函数商类似于(<一个href=”#EEq2">3</一个>),导致以下公式:<年代pan class="equation" id="EEq7"> <svg height="112.8" id="M65" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 112.8" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,112.8)"> <g transform="translate(72,18.24)"> <text transform="matrix(1,0,0,-1,82.65,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代pan> </text> <text transform="matrix(1,0,0,-1,75.87,40.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,80.81,37.87)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 6.25px; " x="2.75088" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,87.45,40.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,95.95,37.87)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,99.84,40.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,106.4,37.87)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 6.25px; " x="2.75088" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,117.43,63.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,113.04,41.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,113.56,33.96)"> <tspan style="font-size: 8.75px; " x="20.559999" y="-29.67"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,129.2,41.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,130.16,33.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,145.35,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,152.4,44.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,223.29,57.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,232.32,62.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1400003"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="9.1400003"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,241.41,57.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,249.21,63.99)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,259.92,57.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,268.94,54.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <g> <path d="m 162.69,50.81 175.95,0" 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,-1,162.69,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.72,40.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="9.1499996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.81,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,188.61,42.01)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,199.31,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,208.34,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,220.21,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,238.32,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,243.19,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="6.54" y="0.49000001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.76,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,264,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> </text> <text transform="matrix(1,0,0,-1,272.63,41.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,280.28,35.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,298.39,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,303.26,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="6.54" y="0.49000001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,316.05,32.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,325.14,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> </text> <text transform="matrix(1,0,0,-1,333.77,41.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,339.84,47.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-204.35001" y="49.57"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,142.54,-5.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,155.11,-1.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="14.115887" y="0"> {</t年代pan> <tspan style="font-size: 12.50px; " x="20.117327" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="26.368828" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="31.570074" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="37.821575" y="0"> }</t年代pan> <tspan style="font-size: 12.50px; " x="45.911015" y="0"> ,</t年代pan> </text> <text transform="matrix(1,0,0,-1,230.55,14.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.16,-8.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.68,-15.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代pan> <tspan style="font-size: 8.75px; " x="10.738704" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,242.32,-1.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,249.37,-5.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.93,-1.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="205.94" y="-25.639999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="210.1035" y="-25.639999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="216.355" y="-25.639999"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="222.60651" y="-25.639999"> )</t年代pan> </text> </g> </g> </svg></span>在第一步中,系数<年代vg height="11.05" id="M66" style="vertical-align:-3.2316pt;width:20.299999px;" version="1.1" viewbox="0 0 20.299999 11.05" width="20.299999" 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pan> </text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>能在类似的方式再决定<年代pan class="equation" id="EEq8"> <svg height="134.375" id="M67" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 134.375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,134.375)"> <g transform="translate(72,35.5)"> <text transform="matrix(1,0,0,-1,81.93,15.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,88.99,12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,101.55,15.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-41.759998"> ⎧</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-31.440001"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-19.9"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-8.3500004"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="3.1900001"> ⎨</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="14.74"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="26.280001"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="37.830002"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="48.09"> ⎩</t年代pan> <tspan style="font-size: 12.50px; " x="115.53" y="-44.849998"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.040001" y="-34.599998"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="26.2915" y="-34.599998"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="41.92025" y="-34.599998"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="45.396084" y="-34.599998"> f</t年代pan> </text> <text transform="matrix(1,0,0,-1,226.11,64.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1400003"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="9.1400003"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,235.2,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,243,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,253.7,59.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,262.73,56.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <g> <path d="m 156.47,52.85 175.96,0" 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,-1,156.47,38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,165.5,42.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="9.1499996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,174.59,38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,182.4,44.05)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,193.1,38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,202.13,34.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,214,38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,232.11,34.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,236.98,38.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="6.54" y="0.49000001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.55,34.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,257.79,38.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> </text> <text transform="matrix(1,0,0,-1,266.41,43.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,274.06,38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,292.17,34.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,297.05,38.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="6.5300002" y="0.49000001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,309.84,34.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,318.93,38.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> </text> <text transform="matrix(1,0,0,-1,327.55,43.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,143.47,11.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="72.050003" y="-10.26"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,224.55,26.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="9.1499996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,231.86,21.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,239.66,27.34)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,250.36,21.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,259.39,18.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <g> <path d="m 156.71,14.16 168.8,0" 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,-1,156.71,-0.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,165.73,3.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.1400003"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="9.1400003"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.04,-0.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,180.84,5.35)"> <tspan style="font-size: 8.75px; " x="0" y="8.71"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,191.55,-0.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,200.57,-3.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,210.66,-0.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,228.77,-3.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,233.64,-0.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="6.54" y="0.49000001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,249.21,-3.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.66,-0.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> </text> <text transform="matrix(1,0,0,-1,261.29,5.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,268.94,-0.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,287.05,-3.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,291.92,-0.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="6.54" y="0.49000001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,304.71,-3.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,312.02,-0.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0.99000001"> 为</t年代pan> </text> <text transform="matrix(1,0,0,-1,320.64,5.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,326.71,11.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-123.46" y="26.969999"> ∀</t年代pan> <tspan style="font-size: 12.50px; " x="-116.45832" y="26.969999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-109.01904" y="26.969999"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="-94.890648" y="26.969999"> {</t年代pan> <tspan style="font-size: 12.50px; " x="-88.889206" y="26.969999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="-82.637703" y="26.969999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-77.436455" y="26.969999"> …</t年代pan> <tspan style="font-size: 12.50px; " x="-62.845455" y="26.969999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-57.631706" y="26.969999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-47.104179" y="26.969999"> }</t年代pan> <tspan style="font-size: 12.50px; " x="-38.327072" y="26.969999"> ⧵</t年代pan> <tspan style="font-size: 12.50px; " x="-29.012339" y="26.969999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-22.235712" y="26.969999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-205.12" y="41.970001"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-198.8685" y="41.970001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-183.23975" y="41.970001"> o</t年代pan> <tspan style="font-size: 12.50px; " x="-177.07578" y="41.970001"> t</t年代pan> <tspan style="font-size: 12.50px; " x="-173.51242" y="41.970001"> h</t年代pan> <tspan style="font-size: 12.50px; " x="-167.26091" y="41.970001"> e</t年代pan> <tspan style="font-size: 12.50px; " x="-161.70958" y="41.970001"> r</t年代pan> <tspan style="font-size: 12.50px; " x="-157.30853" y="41.970001"> w</t年代pan> <tspan style="font-size: 12.50px; " x="-148.28136" y="41.970001"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="-144.80553" y="41.970001"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="-139.94186" y="41.970001"> e</t年代pan> <tspan style="font-size: 12.50px; " x="-134.39053" y="41.970001"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="141.16" y="-4.0999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="145.3235" y="-4.0999999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="151.575" y="-4.0999999"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="157.82649" y="-4.0999999"> )</t年代pan> </text> </g> </g> </svg></span>在第二步中,我们应用综合性CSP算法部分中讨论<一个href=”#sec2">2</一个>最大化的内在和(<一个href=”#EEq7">15</一个>)对<年代vg height="11.3625" id="M68" style="vertical-align:-3.2316pt;width:17.9625px;" version="1.1" viewbox="0 0 17.9625 11.3625" width="17.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="11.3625" id="M69" style="vertical-align:-3.2316pt;width:19.299999px;" version="1.1" viewbox="0 0 19.299999 11.3625" width="19.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>属于各自的学科集群<年代vg height="10.7375" id="M70" 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pan> </text> </g> </g> </svg>。这就完成了算法的两个步骤。然而,仍有小问题,第一步是科目的向量<年代vg height="11.3625" id="M71" style="vertical-align:-3.2316pt;width:17.075001px;" version="1.1" viewbox="0 0 17.075001 11.3625" width="17.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>未知的对象属于集群<年代vg height="10.7375" id="M72" 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pan> </text> </g> </g> </svg>。这是因为在第二步计算<年代vg height="11.3625" id="M73" style="vertical-align:-3.2316pt;width:19.299999px;" version="1.1" viewbox="0 0 19.299999 11.3625" width="19.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>只属于主题<年代vg height="10.7375" id="M74" 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pan> </text> </g> </g> </svg>集群。为此,我们仍然需要优化的商(<一个href=”#EEq7">15</一个>为每个主题分别对)<年代vg height="11.3625" id="M75" style="vertical-align:-3.2316pt;width:17.075001px;" version="1.1" viewbox="0 0 17.075001 11.3625" width="17.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>和固定<年代vg height="11.35" id="M76" style="vertical-align:-3.22282pt;width:15.725px;" version="1.1" viewbox="0 0 15.725 11.35" width="15.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.35)"> <g transform="translate(72,-62.92)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>为每一个<年代vg height="13" id="M77" style="vertical-align:-1.95624pt;width:29.7875px;" version="1.1" viewbox="0 0 29.7875 13" width="29.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13)"> <g transform="translate(72,-61.6)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3015118" y="0"> ≠</t年代pan> <tspan style="font-size: 12.50px; " x="16.954067" y="0"> </t年代pan> </text> </g> </g> </svg>(<年代vg height="10.7375" id="M78" 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pan> </text> </g> </g> </svg>代表集群主体所属)。</p> <p>最后,我们也要找到一个好的初始化的变量。为此,我们使用聚类算法中描述的部分<一个href=”#sec3">3</一个>并将其应用在科目的过滤器与CSP的基本算法计算。这给了我们一个集群的初始估计系数<年代vg height="11.05" id="M79" style="vertical-align:-3.2316pt;width:20.299999px;" version="1.1" viewbox="0 0 20.299999 11.05" width="20.299999" 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pan> </text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>。我们还可以使用集群中心以及它们之间的区别和科目的过滤器来初始化<年代vg height="11.3625" id="M80" style="vertical-align:-3.2316pt;width:17.9625px;" version="1.1" viewbox="0 0 17.9625 11.3625" width="17.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.92,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="11.3625" id="M81" style="vertical-align:-3.2316pt;width:19.299999px;" version="1.1" viewbox="0 0 19.299999 11.3625" width="19.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0"> </t年代pan> </text> </g> </g> </svg>,分别。</p> <h4 id="experiments">5。实验</h4><h5我d="sec5.1">5.1。模拟数据</h5><p>模拟数据生成两个集群的20相似的任务。每个任务的训练集包含两个条件的数据,每个条件计算15个样本。源产生的变量是一个二维高斯分布与零均值和协方差矩阵依赖条件,但同样的集群和所有任务,<年代pan class="equation" id="eq9"> <svg height="62.637501" id="M82" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 62.637501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,62.6375)"> <g transform="translate(72,-21.89)"> <text transform="matrix(1,0,0,-1,128.41,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,136.21,48.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,150.39,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-13.08"> ⎛</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-2.23"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="8.6099997"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="19.4"> ⎝</t年代pan> <tspan style="font-size: 12.50px; " x="36.150002" y="-13.08"> ⎞</t年代pan> <tspan style="font-size: 12.50px; " x="36.150002" y="-2.23"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="36.150002" y="8.6099997"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="36.150002" y="19.4"> ⎠</t年代pan> <tspan style="font-size: 12.50px; " x="17.66" y="-10.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="29.887934" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="17.66" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="29.887934" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="43.860001" y="7.1054274e-015"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="68.978523" y="7.1054274e-015"> Σ</t年代pan> </text> <text transform="matrix(1,0,0,-1,227.18,48.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="2.9144161" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,241.36,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-13.08"> ⎛</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="-2.23"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="8.6099997"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="19.4"> ⎝</t年代pan> <tspan style="font-size: 12.50px; " x="36.139999" y="-13.08"> ⎞</t年代pan> <tspan style="font-size: 12.50px; " x="36.139999" y="-2.23"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="36.139999" y="8.6099997"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="36.139999" y="19.4"> ⎠</t年代pan> <tspan style="font-size: 12.50px; " x="17.66" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="29.887934" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="17.66" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="29.887934" y="14.38"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="43.849998" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="226.50999" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="230.67349" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="236.925" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="243.1765" y="0"> )</t年代pan> </text> </g> </g> </svg></span>混合矩阵的列也从二维高斯分布,生成参数化的各向同性的低方差协方差矩阵(<年代vg height="14.375" id="M83" style="vertical-align:-0.3135pt;width:54.099998px;" version="1.1" viewbox="0 0 54.099998 14.375" width="54.099998" 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,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="19.804752" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="26.056252" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.64,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 4</t年代pan> </text> </g> </g> </svg>)。手段是固定的两个集群和不同,但相同的所有任务在同一集群<年代pan class="equation" id="eq10"> <svg height="136.3625" id="M84" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 136.3625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,136.3625)"> <g transform="translate(72,37.09)"> <text transform="matrix(1,0,0,-1,143.81,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,152.78,40.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,161.13,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="-13.08"> ⎛</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="-2.23"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="8.6099997"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="19.4"> ⎝</t年代pan> <tspan style="font-size: 12.50px; " x="100.97" y="-13.08"> ⎞</t年代pan> <tspan style="font-size: 12.50px; " x="100.97" y="-2.23"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="100.97" y="8.6099997"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="100.97" y="19.4"> ⎠</t年代pan> <tspan style="font-size: 12.50px; " x="108.68" y="7.1054274e-015"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-17.32" y="58.98"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.940001" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.1915" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="31.317249" y="-10.63"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="37.568748" y="-10.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="43.820251" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="50.071751" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="66.575706" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="72.827209" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.952957" y="-10.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="82.20446" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="88.455963" y="-10.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="94.707458" y="-10.63"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="17.66" y="14.38"> −</t年代pan> <tspan style="font-size: 12.50px; " x="26.224554" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="32.476055" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="35.601807" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="41.853306" y="14.38"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="48.104805" y="14.38"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="54.356304" y="14.38"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="66.584236" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="72.835739" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.961487" y="14.38"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="82.21299" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="88.464493" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="94.715988" y="14.38"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,152.78,-18.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,161.13,-15.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="-13.08"> ⎛</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="-2.24"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="8.6099997"> ⎜</t年代pan> <tspan style="font-size: 12.50px; " x="12.03" y="19.4"> ⎝</t年代pan> <tspan style="font-size: 12.50px; " x="100.97" y="-13.08"> ⎞</t年代pan> <tspan style="font-size: 12.50px; " x="100.97" y="-2.24"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="100.97" y="8.6099997"> ⎟</t年代pan> <tspan style="font-size: 12.50px; " x="100.97" y="19.4"> ⎠</t年代pan> <tspan style="font-size: 12.50px; " x="108.68" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.940001" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.1915" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="31.317249" y="-10.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="37.568748" y="-10.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="43.820251" y="-10.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="50.071751" y="-10.63"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="66.575706" y="-10.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="72.827209" y="-10.63"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.952957" y="-10.63"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="82.20446" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="88.455963" y="-10.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="94.707458" y="-10.63"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="17.66" y="14.38"> −</t年代pan> <tspan style="font-size: 12.50px; " x="26.224554" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="32.476055" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="35.601807" y="14.38"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="41.853306" y="14.38"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="48.104805" y="14.38"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="54.356304" y="14.38"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="66.584236" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="72.835739" y="14.38"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="75.961487" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="82.21299" y="14.38"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="88.464493" y="14.38"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="94.715988" y="14.38"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="306.73999" y="-29.49"> (</t年代pan> <tspan style="font-size: 12.50px; " x="310.9035" y="-29.49"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="317.155" y="-29.49"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="323.40649" y="-29.49"> )</t年代pan> </text> </g> </g> </svg></span>我们还添加了一些噪音与零均值和方差非常低(<年代vg height="14.375" id="M85" style="vertical-align:-0.3135pt;width:54.099998px;" version="1.1" viewbox="0 0 54.099998 14.375" width="54.099998" 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,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="19.804752" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="26.056252" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.64,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 3</t年代pan> </text> </g> </g> </svg>)混合观测。一个样本训练集显示在图中<一个href=”//www.newsama.com/journals/cin/2011/217987/fig1/" target="_blank">1(一)</一个>。与285年创建一个类似的测试集数据点的条件。然后我们申请的基本CSP (bCSP)方法在每个这些任务分别和比较它与集群综合性版本(clmtCSP)。CSP的基本解决方案是第一显示25(40)的任务图<一个href=”//www.newsama.com/journals/cin/2011/217987/fig1/" target="_blank">1 (b)</一个>。的最终解决集群综合性学习方法如图<一个href=”//www.newsama.com/journals/cin/2011/217987/fig1/" target="_blank">1 (c)</一个>。在这个玩具的例子中,我们没有对具体执行preclustering过滤器来找到一个好的初始化。相反,前20个任务被认为是(或初始化)属于第一个集群和过去的20任务被认为是属于第二个集群。通过这种方式,我们可以检查的算法能够找到正确的集群。图<一个href=”//www.newsama.com/journals/cin/2011/217987/fig1/" target="_blank">1 (c)</一个>告诉我们,该算法完全可以将任务分配到正确的集群。然而,它是不完美的,你可以看到任务的第三行第二列。此外,可以看到,椭圆的主轴后更好地结合应用clmtCSP算法相比bCSP解决方案。量化这两种方法之间的区别,我们计算估计的方差比率(纯粹的观察),导致来源<年代pan class="equation" id="eq11"> <svg height="65.550003" id="M86" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 65.550003" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,65.55)"> <g transform="translate(72,-19.56)"> <text transform="matrix(1,0,0,-1,110.17,57.08)"> <tspan style="font-size: 12.50px; " x="25.690001" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.459999" y="-2.6500001"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.060001" y="0"> Σ</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代pan> </text> <text 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</svg></span>分别对每个源。这些比率的计算集群。因为来源可以切换和订单不一定是相同的对于这两种方法,我们从高到低排序比率。然后比较这两个比例最高的两种方法,是两个最低。这些结果总结每个集群的箱线图,图<一个href=”//www.newsama.com/journals/cin/2011/217987/fig2/" target="_blank">2</一个>。我们可以看到,中位数clmtCSP总是更大比例的方法。成对魏克森讯号等级测试拒绝平等中位数的假说来源和两个集群。相应的<年代vg height="10.325" id="M87" style="vertical-align:-0.0pt;width:16.9625px;" version="1.1" viewbox="0 0 16.9625 10.325" width="16.9625" 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pan> </text> </g> </g> </svg>值给出图<一个href=”//www.newsama.com/journals/cin/2011/217987/fig2/" target="_blank">2</一个>。</p> <div class="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)训练集”n一个米e=”217987。f我g.001a" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.001a.jpg"> <br> <strong>(一)训练集</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b) bCSP”n一个米e=”217987。f我g.001b" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.001b.jpg"> <br> <strong>(b) bCSP</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(c) clmtCSP”n一个米e=”217987。f我g.001c" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.001c.jpg"> <br> <strong>(c) clmtCSP</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) Training set"><img alt="(一)训练集”n一个米e=”217987。f我g.001a" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.001a.jpg"><br><strong>(一)训练集</年代trong></button> <button class="partial-carousel-dot" aria-label="(b) bCSP"><img alt="(b) bCSP”n一个米e=”217987。f我g.001b" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.001b.jpg"><br><strong>(b) bCSP</年代trong></button> <button class="partial-carousel-dot" aria-label="(c) clmtCSP"><img alt="(c) clmtCSP”n一个米e=”217987。f我g.001c" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.001c.jpg"><br><strong>(c) clmtCSP</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pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/217987/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> (一个)显示了用于计算的训练集bCSP和clmtCSP过滤器。数据点本身并不是策划,而不是我们只画出轮廓数据的标准差估计协方差矩阵,结合相应的主向量(代表椭圆的主轴)。蓝色和黑色轮廓对应于第一节课或条件,而绿色和红色轮廓代表其他类。计算滤波器的目标是校长向量对齐到轴。结果bCSP和clmtCSP所示(b)和(c)的数据,分别。这里,根据轮廓表示标准偏差估计协方差矩阵的“纯粹的”来源。关于clmtCSP方法,如果轮廓画在蓝色和绿色,这意味着他们已经估计是在第一个集群根据算法。如果它是红色和黑色,任务估计属于第二个集群。真正的集群数量在每一个次要情节的称号。</t一个ble> </div> </div> </div> <div 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="(一)bcsp”n一个米e=”217987。f我g.002a" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.002a.jpg"> <br> <strong>(一)bcsp</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b) clmtcsp”n一个米e=”217987。f我g.002b" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.002b.jpg"> <br> <strong>(b) clmtcsp</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig2"> <button class="partial-carousel-dot" aria-label="(a) bcsp"><img alt="(一)bcsp”n一个米e=”217987。f我g.002a" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.002a.jpg"><br><strong>(一)bcsp</年代trong></button> <button class="partial-carousel-dot" aria-label="(b) clmtcsp"><img alt="(b) clmtcsp”n一个米e=”217987。f我g.002b" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.002b.jpg"><br><strong>(b) clmtcsp</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig2"> <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2</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/217987/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="10.325" id="M88" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 16.9625 10.325" width="16.9625" 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pan> </text> </g> </g> </svg> <svg height="7.1624999" id="M89" 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pan> </text> </g> </g> </svg> <table> (a)比较方差比率与clmtCSP bCSP解决方案的解决方案在第一个集群,而(b)使比较第二个集群的任务。酒吧的数量高于或低于每一对的值根据配对魏克森讯号等级测试。蜱虫的标签上的数字后缀设在表示源数量。</t一个ble> </div> </div> </div> <h5 id="sec5.2">5.2。实验数据集</h5><p>我们使用的实验数据集数据第三(BCIC3数据集(BCI竞争<一个href=”http://www.bbci.de/competition/iii/" target="_blank">http://www.bbci.de/competition/iii/</一个>你可以找到的数据集和结果3 e BCI)的竞争,更准确地说数据集IVa和14个科目记录的数据集马普学会生物控制论(MPI的数据集)。</p> <p>BCI竞争的一组包含数据从118个电极记录受试者执行两个任务:右手运动图像和图像。中包括五个主题集和每个主题记录280次试验。我们采取固定测试集的最后180试验而第一100保留构造训练集。限制的数量需要计算的参数优化算法,通道的数量减少到22。选择的是Fp1、Fpz Fp2, F7, F3, F4, Fz, F8, T7, C3, C4、Cz, T8, P7, P3, P4, Pz, P8, POz, O1,奥兹和O2。</p> <p>在MPI组,每个主题进行30左手运动图像试验和30右手运动图像试验。这是重复一次测试集产生的总共120试验/主题。相同的电极作为子集除了前两个渠道,没有记录的一些科目。</p> <p>BCIC3只有五个科目的数据集,我们假设所有科目是相似的。因此,我们将简单地应用第一个算法,即mtCSP。然而,MPI数据集包含太多的科目假设它们都是相似的。因此,我们将运用基于集群的“clmtCSP”方法与一个预定义的集群的数量,即三个。四个集群似乎只有14个科目太多,因为这可能会导致一些集群很少科目。另一方面,我们没有选择两个原因的复杂性增加每个集群对象的数量,因此问题的维数(<一个href=”#EEq3">4</一个>)。在这个阶段,优化算法来解决非凸问题(<一个href=”#EEq3">4</一个>)不能满足如此高的维度。</p> <p>所有信号都是带通过滤8至30 Hz。权衡参数<年代vg height="14.475" id="M90" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.475" id="M91" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>确定通过5倍交叉验证。对于每一个主题,只有两个空间滤波器计算:一个为每个类。交叉验证完成下列组参数:<年代vg height="17.887501" id="M92" style="vertical-align:-3.13504pt;width:333.78751px;" version="1.1" viewbox="0 0 333.78751 17.887501" width="333.78751" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.31,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.34,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-39.99,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="24.280827" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-9.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 4</t年代pan> </text> <text transform="matrix(1,0,0,-1,1.42,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,19.13,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,30,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,47.72,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,58.59,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,76.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,87.17,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,116.34,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,121.22,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,138.93,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,143.8,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,161.52,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,166.39,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,184.1,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代pan> </text> <text transform="matrix(1,0,0,-1,188.98,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代pan> </text> </g> </g> </svg>。平均每个折叠的性能测量的精度(在所有科目)的线性判别式(LDA)分类器折叠。鉴于LDA的已知良好的性能在motor-imagery实验中,我们不仅用它来得分每一个褶皱,也是最终的分类器。</p> <p>图<一个href=”//www.newsama.com/journals/cin/2011/217987/fig3/" target="_blank">3</一个>给一些交叉验证情节BCIC3 mtCSP算法,设置显示的平均精度(在主题和折叠)每个参数设置。很明显,对于一个低数量的训练试验(10类),参数值偏向于促进共享过滤器组件,而惩罚科目的组件。更多的培训试验每课(约100),很明显,往往会受到特定的参数值。MPI的数据集,我们修复<年代vg height="14.6" id="M93" style="vertical-align:-3.13504pt;width:41.875px;" version="1.1" viewbox="0 0 41.875 14.6" width="41.875" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>来降低计算的要求。根据图<一个href=”//www.newsama.com/journals/cin/2011/217987/fig3/" target="_blank">3</一个>,这似乎是一个不错的选择的参数值在网格的边界产生最有趣的结果。此外,固定定义的线<年代vg height="14.6" id="M94" style="vertical-align:-3.13504pt;width:77.037498px;" version="1.1" viewbox="0 0 77.037498 14.6" width="77.037498" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="40.159637" y="0"> 1</t年代pan> </text> </g> </g> </svg>显示最可变性,而定义的线固定<年代vg height="14.6" id="M95" style="vertical-align:-3.13504pt;width:77.037498px;" version="1.1" viewbox="0 0 77.037498 14.6" width="77.037498" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="40.159637" y="0"> 1</t年代pan> </text> </g> </g> </svg>似乎并没有多大的改变<年代vg height="14.475" id="M96" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>是多种多样的。</p> <div class="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="(一)BCIC3数据集”n一个米e=”217987。f我g.003a" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.003a.jpg"> <br> <strong>(一)BCIC3数据集</年代trong> </div> <div class="partial-carousel--single-image"> <img alt="(b) BCIC3数据集”n一个米e=”217987。f我g.003b" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.003b.jpg"> <br> <strong>(b) BCIC3数据集</年代trong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig3"> <button class="partial-carousel-dot" aria-label="(a) BCIC3 data set"><img alt="(一)BCIC3数据集”n一个米e=”217987。f我g.003a" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.003a.jpg"><br><strong>(一)BCIC3数据集</年代trong></button> <button class="partial-carousel-dot" aria-label="(b) BCIC3 data set"><img alt="(b) BCIC3数据集”n一个米e=”217987。f我g.003b" src="https://static-01.hindawi.com/articles/cin/volume-2011/217987/figures/217987.fig.003b.jpg"><br><strong>(b) BCIC3数据集</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig3"> <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3</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/217987/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="14.475" id="M97" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg> <svg height="14.475" id="M98" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg> <table> 每个参数的组合交叉验证精度和BCIC3数据集。我们进行5倍交叉验证/主题。平均结果在折叠和所有科目给最终结果绘制的图。</t一个ble> </div> </div> </div> <p>每个主题的结果分别给出了表<一个href=”//www.newsama.com/journals/cin/2011/217987/tab1/" target="_blank">1</一个>和<一个href=”//www.newsama.com/journals/cin/2011/217987/tab2/" target="_blank">2</一个>BCIC3和MPI的数据集,分别。每个表的头参数的值<年代vg height="14.475" id="M99" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和/或<年代vg height="14.475" id="M100" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>通过交叉验证确定。还要注意,的意思是只计算在这些学科的方法之一至少达到高于机会水平(180次试验的测试集,我们可以修复的机会水平以56%的精度为MPI BCIC3集。数据集,我们设置了机会水平为60%)的精度。</p> <div class="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="9"> <hr></td> </tr> <tr> <td align="left"></td> <td align="center" colspan="2">5试验</td> <td align="center" colspan="2">10个试验</td> <td align="center" colspan="2">20次试验</td> <td align="center" colspan="2">30试验</td> </tr> <tr> <td align="left"></td> <td align="center" colspan="2"> <svg height="17.887501" id="M101" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.275002 17.887501" width="63.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 3</t年代pan> </text> </g> </g> </svg>,<年代vg height="17.887501" id="M102" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.275002 17.887501" width="63.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> </g> </g> </svg></td> <td align="center" colspan="2"> <svg height="17.887501" id="M103" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.275002 17.887501" width="63.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 4</t年代pan> </text> </g> </g> </svg>,<年代vg height="17.887501" id="M104" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 55.787498 17.887501" width="55.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg></td> <td align="center" colspan="2"> <svg height="17.887501" id="M105" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.275002 17.887501" width="63.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 3</t年代pan> </text> </g> </g> </svg>,<年代vg height="17.887501" id="M106" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.275002 17.887501" width="63.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> </g> </g> </svg></td> <td align="center" colspan="2"> <svg height="17.887501" id="M107" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.275002 17.887501" width="63.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 4</t年代pan> </text> </g> </g> </svg>,<年代vg height="17.887501" id="M108" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 55.787498 17.887501" width="55.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg></td> </tr> <tr> <td align="left">主题</td> <td align="center">bCSP</td> <td align="center">mtCSP</td> <td align="center">bCSP</td> <td align="center">mtCSP</td> <td align="center">bCSP</td> <td align="center">mtCSP</td> <td align="center">bCSP</td> <td align="center">mtCSP</td> </tr> <tr> <td align="center" colspan="9"> <hr></td> </tr> <tr> <td align="left"><i>aa</我></td> <td align="center">0.49</td> <td align="center">0.73</td> <td align="center">0.54</td> <td align="center">0.64</td> <td align="center">0.66</td> <td align="center">0.71</td> <td align="center">0.61</td> <td align="center">0.69</td> </tr> <tr> <td align="left"><i>艾尔</我></td> <td align="center">0.80</td> <td align="center">0.73</td> <td align="center">0.95</td> <td align="center">0.93</td> <td align="center">0.95</td> <td align="center">0.94</td> <td align="center">0.94</td> <td align="center">0.94</td> </tr> <tr> <td align="left"><i>av</我></td> <td align="center">0.56</td> <td align="center">0.58</td> <td align="center">0.59</td> <td align="center">0.63</td> <td align="center">0.44</td> <td align="center">0.62</td> <td align="center">0.56</td> <td align="center">0.64</td> </tr> <tr> <td align="left"><i>亚历山大-伍尔兹</我></td> <td align="center">0.69</td> <td align="center">0.57</td> <td align="center">0.69</td> <td align="center">0.56</td> <td align="center">0.66</td> <td align="center">0.58</td> <td align="center">0.55</td> <td align="center">0.54</td> </tr> <tr> <td align="left"><i>唉</我></td> <td align="center">0.92</td> <td align="center">0.86</td> <td align="center">0.84</td> <td align="center">0.93</td> <td align="center">0.85</td> <td align="center">0.85</td> <td align="center">0.88</td> <td align="center">0.87</td> </tr> <tr> <td align="center" colspan="9"> <hr></td> </tr> <tr> <td align="left">的意思是</td> <td align="center">0.69</td> <td align="center">0.69</td> <td align="center">0.72</td> <td align="center">0.74</td> <td align="center">0.71</td> <td align="center">0.74</td> <td align="center">0.75</td> <td align="center">0.79</td> </tr> <tr class="table-tr"> <td colspan="9"> <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pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/217987/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 每BCI竞争的主题分类精度数据集。</div> </div> </div> <div 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="7"> <hr></td> </tr> <tr> <td align="left"></td> <td align="center" colspan="2">5试验</td> <td align="center" colspan="2">10个试验</td> <td align="center" colspan="2">20次试验</td> </tr> <tr> <td align="left"></td> <td align="center" colspan="2"><span style="width: 63.275002px;"> <svg height="17.887501" id="M109" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.275002 17.887501" width="63.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> </text> </g> </g> </svg></span></td> <td align="center" colspan="2"><span style="width: 63.275002px;"> <svg height="17.887501" id="M110" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.275002 17.887501" width="63.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 2</t年代pan> </text> </g> </g> </svg></span></td> <td align="center" colspan="2"><span style="width: 63.275002px;"> <svg height="17.887501" id="M111" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.275002 17.887501" width="63.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 4</t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">主题</td> <td align="center">bCSP</td> <td align="center">clmtCSP</td> <td align="center">bCSP</td> <td align="center">clmtCSP</td> <td align="center">bCSP</td> <td align="center">clmtCSP</td> </tr> <tr> <td align="center" colspan="7"> <hr></td> </tr> <tr> <td align="left">1</td> <td align="center">0.80</td> <td align="center">0.68</td> <td align="center">0.78</td> <td align="center">0.73</td> <td align="center">0.85</td> <td align="center">0.85</td> </tr> <tr> <td align="left">2</td> <td align="center">0.85</td> <td align="center">0.83</td> <td align="center">0.83</td> <td align="center">0.77</td> <td align="center">0.87</td> <td align="center">0.85</td> </tr> <tr> <td align="left">3</td> <td align="center">0.45</td> <td align="center">0.43</td> <td align="center">0.53</td> <td align="center">0.57</td> <td align="center">0.58</td> <td align="center">0.60</td> </tr> <tr> <td align="left">4</td> <td align="center">0.58</td> <td align="center">0.53</td> <td align="center">0.72</td> <td align="center">0.75</td> <td align="center">0.77</td> <td align="center">0.77</td> </tr> <tr> <td align="left">5</td> <td align="center">0.53</td> <td align="center">0.47</td> <td align="center">0.52</td> <td align="center">0.48</td> <td align="center">0.62</td> <td align="center">0.60</td> </tr> <tr> <td align="left">6</td> <td align="center">0.58</td> <td align="center">0.67</td> <td align="center">0.60</td> <td align="center">0.60</td> <td align="center">0.70</td> <td align="center">0.70</td> </tr> <tr> <td align="left">7</td> <td align="center">0.83</td> <td align="center">0.92</td> <td align="center">0.90</td> <td align="center">0.92</td> <td align="center">0.95</td> <td align="center">0.95</td> </tr> <tr> <td align="left">8</td> <td align="center">0.38</td> <td align="center">0.52</td> <td align="center">0.48</td> <td align="center">0.48</td> <td align="center">0.53</td> <td align="center">0.53</td> </tr> <tr> <td align="left">9</td> <td align="center">0.57</td> <td align="center">0.70</td> <td align="center">0.58</td> <td align="center">0.62</td> <td align="center">0.63</td> <td align="center">0.63</td> </tr> <tr> <td align="left">10</td> <td align="center">0.68</td> <td align="center">0.53</td> <td align="center">0.60</td> <td align="center">0.62</td> <td align="center">0.63</td> <td align="center">0.60</td> </tr> <tr> <td align="left">11</td> <td align="center">0.50</td> <td align="center">0.53</td> <td align="center">0.42</td> <td align="center">0.52</td> <td align="center">0.40</td> <td align="center">0.43</td> </tr> <tr> <td align="left">12</td> <td align="center">0.52</td> <td align="center">0.68</td> <td align="center">0.65</td> <td align="center">0.70</td> <td align="center">0.63</td> <td align="center">0.63</td> </tr> <tr> <td align="left">13</td> <td align="center">0.62</td> <td align="center">0.60</td> <td align="center">0.63</td> <td align="center">0.58</td> <td align="center">0.57</td> <td align="center">0.60</td> </tr> <tr> <td align="left">14</td> <td align="center">0.53</td> <td align="center">0.53</td> <td align="center">0.50</td> <td align="center">0.47</td> <td align="center">0.55</td> <td align="center">0.57</td> </tr> <tr> <td align="center" colspan="9"> <hr></td> </tr> <tr> <td align="left">的意思是</td> <td align="center">0.68</td> <td align="center">0.70</td> <td align="center">0.70</td> <td align="center">0.70</td> <td align="center">0.71</td> <td align="center">0.71</td> </tr> <tr class="table-tr"> <td colspan="7"> <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pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/217987/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 分类精度/ MPI的主题。</div> </div> </div> <p>我们首先注意到的BCIC3集5试验(从现在起,我们国家培训试验每个类的数量,例如,当我们提到5培训试验,我们的意思是5试验每个类,因此10。)综合性版本的影响相对较低,虽然这是我们怀疑的地方是最大的影响。然而,对于一些科目,如主题<我>一个一个</我>影响是大量从机会水平精度远高于70%。另一方面,有话题<我>亚历山大-伍尔兹</我>精度下降的机会水平时采用综合性的版本。这个话题,然而,似乎从未从综合性学习中受益。这两个科目可以给我们一些了解失败的原因,我们认为我们确定参数的方式<年代vg height="14.475" id="M112" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.475" id="M113" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>。所有科目,因此这样做是在全球范围内的值是相同的。显然,这些参数应分别确定为每一个新的主题。理想情况下将包括五个试验的“新”主题的训练集,其他科目的所有训练试验并为每个主题重复这个过程。另一方面,这将要求我们确定参数每学科独立一组只有5个试验每个类,这是容易不稳定。</p> <p>这两种方法之间的区别变得明显在10的情况下训练试验mtCSP方法达到更好的或同等精度相比bCSP方法在所有科目,除了主题<我>亚历山大-伍尔兹</我>。只有五个科目,我们不能显示配对魏克森讯号等级的区别是重要的测试。</p> <p>表<一个href=”//www.newsama.com/journals/cin/2011/217987/tab2/" target="_blank">2</一个>显示了基于集群的结果mtCSP方法在所有14个科目。看选择的参数值<年代vg height="14.475" id="M114" style="vertical-align:-3.13504pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 14.475" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>,我们可以看到,大多数惩罚当只有五个训练科目的过滤器组件试验,至少惩罚当20个训练试验时是可用的。这反映在结果几乎没有区别bCSP和clmtCSP 20训练试验。然而,有相当一些五试验两种方法之间的区别。不幸的是,成对魏克森讯号等级测试(只考虑这些学科的哪一个方法执行机会以上)不显示显著差异。注意(5培训试验)的情况下只有8个主题都包含在测试。</p> <h4 id="discussion-and-future-work">6。讨论和未来的工作</h4><p>我们提出了一个综合性扩展基本的CSP算法以减少训练试验和提高性能通过学习学科之间空间过滤器。它涉及一个凸优化问题,因此全球解决方案是不能保证当用人标准的优化技术。然而,这种笔凸凸的优化比例优化理论中是一个热门话题。我们可以预见,在未来,实现将可用,保证全局收敛性和可伸缩的处理高维问题。作者在<一个href=”#B15">15</一个>]目前这种看似小型解决方案问题。</p> <p>提出方法的主要缺点是,我们必须执行交叉验证选择好的参数值。首先,这需要时间来计算,渲染方法不切实际的在这段时间内一个可以记录多个数据帧计算好过滤器。其次,需要足够的数据可以通过交叉验证来确定参数值。这当然是相反,目的是提出的算法来减少训练试验。为了找到指标方法的潜力的训练实验,我们进行了交叉验证的平均得分在几个折叠和主题。这将导致更加稳定和可靠的估计的参数值。然后我们选择的参数值相同的主题。然而,需要交叉验证可以避免采用贝叶斯框架。为了学习这个框架模型在几个学科,共享先知先觉的使用将是未来研究的主题。</p> <p>一个悬而未决的问题是如何比较和其他CSP变体,学习其他科目<一个href=”#B16">16</一个>]。后一种方法计算过滤器通过结合几个科目的协方差矩阵。</p> <p>由于我们执行交叉验证的方式,是不可能显示方法的真正潜力。然而,一些研究结果表明,CSP(基于集群)综合性学习导致对某些科目有明显改善。一些受试者患有这些方法可以避免如果权衡参数可以单独为每个新主题选择可靠的训练数据。</p> <p>最后,我们想要添加的这种方式包括集群优化问题可以用于基于集群的综合性分类器。请注意,费舍尔的判别分析<一个href=”#B17">17</一个>可以写成一个广义瑞利商与广义特征值分解,从而得到解决,类似于CSP。而不是使用的商(<一个href=”#EEq2">3</一个>),我们可以插入一个修改版费雪的比率。</p> </div> <div class="xml-content"> <h4 class="references" id="references">引用</h4><ol> <li id="B1">洛杉矶Farwell和e . 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Guan" target="_blank">谷歌学术搜索</一个></年代pan></li> <li id="B17">c .主教<我>模式识别和机器学习</我>施普林格,柏林,德国,2008年。<年代pan class="reflinks"></span></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</h4><p>版权©2011 Dieter Devlaminck 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> </div> </div> </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 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height="24"><span class="sc-dRFtgE jrsDZP">订单打印副本</年代pan><span class="sc-gkFcWv gWTCXQ">订单</年代pan></span><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pan>2719年</年代pan> </div> <div> 下载<年代pan>1930年</年代pan> </div> </div> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2011/217987" data-style="small_circle"></span>引用</div> </div> </div> <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/10.1155/2011/217987&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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