Cascade Support Vector Machines with Dimensionality Reduction

<div>Pseudocode of ECM algorithm. In each cascade level, the <svg height="9.89089pt" id="M58" style="vertical-align:-0.2129898pt" version="1.1" viewbox="-0.0498162 -9.6779 7.64706 9.89089" width="7.64706pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555"></glyph.data></g></svg>-dimensional patterns <svg height="9.31156pt" id="M59" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -5.88377 9.81786 9.31156" width="9.81786pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M494 0V32C450 38 426 53 393 105L296 260C330 305 354 338 375 361C411 396 421 401 476 410V442H293V410C332 402 337 394 323 371C311 351 295 324 274 293L227 371C213 393 218 402 252 410V442H16V410C70 402 80 391 108 344L196 199C166 159 140 123 115 95C81 54 61 43 7 32V0H196V32C156 41 150 53 167 81C182 105 199 138 219 166L269 79C287 49 283 38 245 32V0H494Z" id="g13-118"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="482" vert-adv-y="482"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,6.53,3.264)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data></g></svg>, which are the pendants of the <svg height="9.7821pt" id="M60" style="vertical-align:-3.57194pt" version="1.1" viewbox="-0.0498162 -6.21016 6.77673 9.7821" width="6.77673pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z" id="g113-114"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="491" vert-adv-y="491"></glyph.data></g></svg>-dimensional support vectors <svg height="13.8019pt" id="M61" style="vertical-align:-3.4278pt" version="1.1" viewbox="-0.0498162 -10.3741 39.9748 13.8019" width="39.9748pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,.163,0)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="470" vert-adv-y="470"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M494 0V32C450 38 426 53 393 105L296 260C330 305 354 338 375 361C411 396 421 401 476 410V442H293V410C332 402 337 394 323 371C311 351 295 324 274 293L227 371C213 393 218 402 252 410V442H16V410C70 402 80 391 108 344L196 199C166 159 140 123 115 95C81 54 61 43 7 32V0H196V32C156 41 150 53 167 81C182 105 199 138 219 166L269 79C287 49 283 38 245 32V0H494Z" id="g13-118"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="482" vert-adv-y="482"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,6.53,3.264)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,13.503,0)"><path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="528" vert-adv-y="528"></glyph.data></g><g transform="matrix(.0136,0,0,-0.0136,24.442,0)"><path d="M712 0L497 285C582 312 628 378 628 466C628 609 518 662 390 662H70V0H236V271H310L505 0H712ZM491 604C551 577 584 532 584 464C584 401 550 345 491 321V604ZM447 320C428 317 411 315 392 315H236V618H397C412 618 432 613 447 610V320ZM626 44H528L363 271C392 271 422 270 451 275L626 44ZM192 44H114V618H192V44Z" id="g197-29"></path><glyph.data ascent="693" descent="-218" horiz-adv-x="747" vert-adv-y="747"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,34.562,-5.984)"><path d="M481 430L460 436C440 442 393 451 366 451C348 451 325 448 313 446C267 437 195 409 147 367C79 308 24 211 24 105C24 37 56 -12 93 -12C121 -12 156 1 199 32C246 66 313 122 349 168H351L286 -147C274 -205 261 -215 210 -224L199 -226L193 -255L438 -243L442 -214L417 -212C364 -208 359 -200 370 -140L433 204C455 324 469 389 481 430ZM391 385C382 336 366 260 358 238C321 178 209 59 143 59C129 59 115 83 115 131C115 207 152 317 220 373C243 392 282 403 314 403C348 403 374 395 391 385Z" id="g50-114"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="499" vert-adv-y="499"></glyph.data></g></svg> of the previous cascade level, are employed as training patterns.</div>

Applied Computational Intelligence and Soft Computing

alg1

Algorithm 1

Algorithm 1: Cascade Support Vector Machines with Dimensionality Reduction 

应用计算智能软计算

级联支持向量机减少分量

算法一