An Improved Kernel Credal Classification Algorithm Based on Regularized Mahalanobis Distance: Application to Microarray Data Analysis

<table class="fixed-width table-group" id="tab2"><tr><td><table class="table"><colgroup><col style="width:7.89em"/><col style="width:2.94em"/><col style="width:2.85em"/><col style="width:3.64em"/><col style="width:3.33em"/><col style="width:3.11em"/><col style="width:3.64em"/><col style="width:3.30em"/><col style="width:3.31em"/><col style="width:3.64em"/></colgroup><tr><td class="thead-hr" colspan="10"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2"> </td><td class="align_center" colspan="3"><b>CCR</b></td><td class="align_center" colspan="3"><b>KCCR</b></td><td class="align_center" colspan="3"><b>MKCCR</b></td></tr><tr class="thead"><td class="align_center"><span style="width: 13.4899ptpx;"><svg height="11.7574pt" id="M143" style="vertical-align:-3.291129pt" version="1.1" viewbox="-0.0498162 -8.46627 13.4899 11.7574" width="13.4899pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M668 26C646 31 631 35 610 64C593 87 572 122 543 176L484 306C568 331 646 391 646 489C646 553 620 593 575 617C533 644 471 650 409 650H139L131 613C216 609 222 604 206 520L134 135C116 53 101 42 25 37L16 0H331L338 37C261 42 249 54 264 136L291 281H318C352 281 365 267 375 235C392 185 416 130 438 87C471 25 501 -8 656 -8L668 26ZM502 485C502 431 477 379 426 347C395 329 361 323 322 323H298L343 558C347 577 351 587 357 593C368 602 384 605 403 605C454 605 502 575 502 485Z" id="g5-83"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.69,3.132)"><path d="M438 367C438 417 399 457 319 457C256 457 186 426 142 394C59 334 22 233 22 144C22 21 97 -12 157 -12C246 -12 326 29 414 118L391 155C342 109 275 73 234 73C181 73 159 115 159 160C159 168 160 178 161 186C262 211 438 256 438 367ZM319 359C319 305 281 262 164 230C176 324 218 383 251 401C257 404 273 408 282 408C289 408 319 396 319 359Z" id="g14-102"></path></g></svg></span></td><td class="align_center"><span style="width: 16.8604ptpx;"><svg height="11.7574pt" id="M144" style="vertical-align:-3.291129pt" version="1.1" viewbox="-0.0498162 -8.46627 16.8604 11.7574" width="16.8604pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M668 26C646 31 631 35 610 64C593 87 572 122 543 176L484 306C568 331 646 391 646 489C646 553 620 593 575 617C533 644 471 650 409 650H139L131 613C216 609 222 604 206 520L134 135C116 53 101 42 25 37L16 0H331L338 37C261 42 249 54 264 136L291 281H318C352 281 365 267 375 235C392 185 416 130 438 87C471 25 501 -8 656 -8L668 26ZM502 485C502 431 477 379 426 347C395 329 361 323 322 323H298L343 558C347 577 351 587 357 593C368 602 384 605 403 605C454 605 502 575 502 485Z" id="g5-83"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.69,3.132)"><path d="M294 607C294 643 272 671 230 671C172 671 143 618 143 593C143 548 173 524 215 524C261 524 294 565 294 607ZM285 104L263 135C232 107 205 93 193 93C185 93 184 106 191 135L247 358C259 406 254 457 224 457C184 457 113 420 28 348L47 315C76 336 101 349 109 349S115 337 109 314L58 109C33 10 61 -12 96 -12C128 -12 209 18 285 104Z" id="g14-106"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.632,3.132)"><path d="M440 180C404 113 397 110 338 110H183L298 220C398 316 438 379 438 456C438 568 354 635 254 635C192 635 138 610 101 572L36 479L69 452C103 500 144 541 204 541C270 541 306 494 306 425C306 350 267 276 197 193C148 136 89 81 36 30V0H440C451 42 463 106 480 167L440 180Z" id="g22-48"></path></g></svg></span></td><td class="align_center"><b>Noise</b></td><td class="align_center"><span style="width: 13.4899ptpx;"><svg height="11.7574pt" id="M145" style="vertical-align:-3.291129pt" version="1.1" viewbox="-0.0498162 -8.46627 13.4899 11.7574" width="13.4899pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M668 26C646 31 631 35 610 64C593 87 572 122 543 176L484 306C568 331 646 391 646 489C646 553 620 593 575 617C533 644 471 650 409 650H139L131 613C216 609 222 604 206 520L134 135C116 53 101 42 25 37L16 0H331L338 37C261 42 249 54 264 136L291 281H318C352 281 365 267 375 235C392 185 416 130 438 87C471 25 501 -8 656 -8L668 26ZM502 485C502 431 477 379 426 347C395 329 361 323 322 323H298L343 558C347 577 351 587 357 593C368 602 384 605 403 605C454 605 502 575 502 485Z" id="g5-83"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.69,3.132)"><path d="M438 367C438 417 399 457 319 457C256 457 186 426 142 394C59 334 22 233 22 144C22 21 97 -12 157 -12C246 -12 326 29 414 118L391 155C342 109 275 73 234 73C181 73 159 115 159 160C159 168 160 178 161 186C262 211 438 256 438 367ZM319 359C319 305 281 262 164 230C176 324 218 383 251 401C257 404 273 408 282 408C289 408 319 396 319 359Z" id="g14-102"></path></g></svg></span></td><td class="align_center"><span style="width: 16.8604ptpx;"><svg height="11.7574pt" id="M146" style="vertical-align:-3.291129pt" version="1.1" viewbox="-0.0498162 -8.46627 16.8604 11.7574" width="16.8604pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M668 26C646 31 631 35 610 64C593 87 572 122 543 176L484 306C568 331 646 391 646 489C646 553 620 593 575 617C533 644 471 650 409 650H139L131 613C216 609 222 604 206 520L134 135C116 53 101 42 25 37L16 0H331L338 37C261 42 249 54 264 136L291 281H318C352 281 365 267 375 235C392 185 416 130 438 87C471 25 501 -8 656 -8L668 26ZM502 485C502 431 477 379 426 347C395 329 361 323 322 323H298L343 558C347 577 351 587 357 593C368 602 384 605 403 605C454 605 502 575 502 485Z" id="g5-83"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.69,3.132)"><path d="M294 607C294 643 272 671 230 671C172 671 143 618 143 593C143 548 173 524 215 524C261 524 294 565 294 607ZM285 104L263 135C232 107 205 93 193 93C185 93 184 106 191 135L247 358C259 406 254 457 224 457C184 457 113 420 28 348L47 315C76 336 101 349 109 349S115 337 109 314L58 109C33 10 61 -12 96 -12C128 -12 209 18 285 104Z" id="g14-106"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.632,3.132)"><path d="M440 180C404 113 397 110 338 110H183L298 220C398 316 438 379 438 456C438 568 354 635 254 635C192 635 138 610 101 572L36 479L69 452C103 500 144 541 204 541C270 541 306 494 306 425C306 350 267 276 197 193C148 136 89 81 36 30V0H440C451 42 463 106 480 167L440 180Z" id="g22-48"></path></g></svg></span></td><td class="align_center"><b>Noise</b></td><td class="align_center"><span style="width: 13.4899ptpx;"><svg height="11.7574pt" id="M147" style="vertical-align:-3.291129pt" version="1.1" viewbox="-0.0498162 -8.46627 13.4899 11.7574" width="13.4899pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M668 26C646 31 631 35 610 64C593 87 572 122 543 176L484 306C568 331 646 391 646 489C646 553 620 593 575 617C533 644 471 650 409 650H139L131 613C216 609 222 604 206 520L134 135C116 53 101 42 25 37L16 0H331L338 37C261 42 249 54 264 136L291 281H318C352 281 365 267 375 235C392 185 416 130 438 87C471 25 501 -8 656 -8L668 26ZM502 485C502 431 477 379 426 347C395 329 361 323 322 323H298L343 558C347 577 351 587 357 593C368 602 384 605 403 605C454 605 502 575 502 485Z" id="g5-83"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.69,3.132)"><path d="M438 367C438 417 399 457 319 457C256 457 186 426 142 394C59 334 22 233 22 144C22 21 97 -12 157 -12C246 -12 326 29 414 118L391 155C342 109 275 73 234 73C181 73 159 115 159 160C159 168 160 178 161 186C262 211 438 256 438 367ZM319 359C319 305 281 262 164 230C176 324 218 383 251 401C257 404 273 408 282 408C289 408 319 396 319 359Z" id="g14-102"></path></g></svg></span></td><td class="align_center"><span style="width: 16.8604ptpx;"><svg height="11.7574pt" id="M148" style="vertical-align:-3.291129pt" version="1.1" viewbox="-0.0498162 -8.46627 16.8604 11.7574" width="16.8604pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M668 26C646 31 631 35 610 64C593 87 572 122 543 176L484 306C568 331 646 391 646 489C646 553 620 593 575 617C533 644 471 650 409 650H139L131 613C216 609 222 604 206 520L134 135C116 53 101 42 25 37L16 0H331L338 37C261 42 249 54 264 136L291 281H318C352 281 365 267 375 235C392 185 416 130 438 87C471 25 501 -8 656 -8L668 26ZM502 485C502 431 477 379 426 347C395 329 361 323 322 323H298L343 558C347 577 351 587 357 593C368 602 384 605 403 605C454 605 502 575 502 485Z" id="g5-83"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.69,3.132)"><path d="M294 607C294 643 272 671 230 671C172 671 143 618 143 593C143 548 173 524 215 524C261 524 294 565 294 607ZM285 104L263 135C232 107 205 93 193 93C185 93 184 106 191 135L247 358C259 406 254 457 224 457C184 457 113 420 28 348L47 315C76 336 101 349 109 349S115 337 109 314L58 109C33 10 61 -12 96 -12C128 -12 209 18 285 104Z" id="g14-106"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.632,3.132)"><path d="M440 180C404 113 397 110 338 110H183L298 220C398 316 438 379 438 456C438 568 354 635 254 635C192 635 138 610 101 572L36 479L69 452C103 500 144 541 204 541C270 541 306 494 306 425C306 350 267 276 197 193C148 136 89 81 36 30V0H440C451 42 463 106 480 167L440 180Z" id="g22-48"></path></g></svg></span></td><td class="align_center"><b>Noise</b></td></tr><tr><td class="thead-hr" colspan="10"><hr/></td></tr><tr><td class="align_left"><b>iris</b> (<svg height="11.7978pt" id="M149" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 39.2293 11.7978" width="39.2293pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 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id="g113-51"></path></g><g transform="matrix(.013,0,0,-0.013,32.789,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g></svg>)</td><td class="align_center">8.67</td><td class="align_center">3.33</td><td class="align_center">0</td><td class="align_center">8.67</td><td class="align_center">3.33</td><td class="align_center">0</td><td class="align_center">8.00</td><td class="align_center">2.67</td><td class="align_center">0</td></tr><tr><td class="align_left"><b>wdbc</b> (<svg height="13.8595pt" id="M150" style="vertical-align:-2.2681pt" version="1.1" viewbox="-0.0498162 -11.5914 50.0076 13.8595" width="50.0076pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z" id="g113-105"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.708,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g><g transform="matrix(.013,0,0,-0.013,15.286,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,26.549,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 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id="g113-42"></path></g></svg></td><td class="align_center">NA</td><td class="align_center">NA</td><td class="align_center">100</td><td class="align_center">8.61</td><td class="align_center">13.71</td><td class="align_center">1.05</td><td class="align_center">7.38</td><td class="align_center">15.64</td><td class="align_center">0</td></tr><tr><td class="align_left"><b>htru2</b><svg height="13.8595pt" id="M151" style="vertical-align:-2.2681pt" version="1.1" viewbox="-0.0498162 -11.5914 50.0076 13.8595" width="50.0076pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 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transform="matrix(.013,0,0,-0.013,37.287,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.013,0,0,-0.013,43.527,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g></svg>)</td><td class="align_center">NA</td><td class="align_center">NA</td><td class="align_center">100</td><td class="align_center">25.53</td><td class="align_center">7.16</td><td class="align_center">2.95</td><td class="align_center">15.04</td><td class="align_center">12.26</td><td class="align_center">0</td></tr><tr class="table-tr"><td colspan="10"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Error rate and imprecision rate with different methods in %.</div>

Computational Intelligence and Neuroscience

tab2

Table 2

Table 2: An Improved Kernel Credal Classification Algorithm Based on Regularized Mahalanobis Distance: Application to Microarray Data Analysis 