Gene Selection via a New Hybrid Ant Colony Optimization Algorithm for Cancer Classification in High-Dimensional Data

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">Gene<sub>id</sub></td><td class="align_center">Gene<sub>1</sub></td><td class="align_center">Gene<sub>2</sub></td><td class="align_center"><span style="width: 15.5623ptpx;"><svg height="4.18388pt" id="M5" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -4.13406 15.5623 4.18388" width="15.5623pt" 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="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.143,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.286,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g></svg></span></td><td class="align_center">Gene<sub><i>N</i></sub></td><td class="align_center">Class label</td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">Sample<sub>1</sub></td><td class="align_center"><i>x</i><sub>11</sub></td><td class="align_center"><i>x</i><sub>12</sub></td><td class="align_center"><span style="width: 15.5623ptpx;"><svg height="4.18388pt" id="M6" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -4.13406 15.5623 4.18388" width="15.5623pt" 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="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.143,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.286,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g></svg></span></td><td class="align_center"><i>x</i><sub>1<i>N</i></sub></td><td class="align_center"><span style="width: 12.0141ptpx;"><svg height="9.39034pt" id="M7" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 12.0141 9.39034" width="12.0141pt" 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="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.942,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg></span></td></tr><tr><td class="align_left">Sample<sub>2</sub></td><td class="align_center"><i>x</i><sub>21</sub></td><td class="align_center"><i>x</i><sub>22</sub></td><td class="align_center"><span style="width: 15.5623ptpx;"><svg height="4.18388pt" id="M8" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -4.13406 15.5623 4.18388" width="15.5623pt" 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="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.143,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.286,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g></svg></span></td><td class="align_center"><i>x</i><sub>2<i>N</i></sub></td><td class="align_center"><span style="width: 12.0141ptpx;"><svg height="9.39034pt" id="M9" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 12.0141 9.39034" width="12.0141pt" 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="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.942,3.132)"><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"></path></g></svg></span></td></tr><tr><td class="align_left">Sample<sub>3</sub></td><td class="align_center"><i>x</i><sub>31</sub></td><td class="align_center"><i>x</i><sub>32</sub></td><td class="align_center"><span style="width: 15.5623ptpx;"><svg height="4.18388pt" id="M10" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -4.13406 15.5623 4.18388" width="15.5623pt" 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="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.143,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.286,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g></svg></span></td><td class="align_center"><i>x</i><sub>3<i>N</i></sub></td><td class="align_center"><span style="width: 12.0141ptpx;"><svg height="9.39034pt" id="M11" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 12.0141 9.39034" width="12.0141pt" 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="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.942,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 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transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td><td class="align_center"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M13" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td><td class="align_center"><span style="width: 3.07474ptpx;"><svg 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transform="matrix(.013,0,0,-0.013,0,0)"><path d="M215 581C215 613 191 638 159 638S103 613 103 581C103 546 126 523 159 523C191 523 215 546 215 581ZM541 255C541 287 517 312 485 312S429 287 429 255C429 220 452 197 485 197C517 197 541 220 541 255ZM867 -71C867 -39 843 -14 811 -14S755 -39 755 -71C755 -106 778 -129 811 -129C843 -129 867 -106 867 -71Z"></path></g></svg></span></td><td class="align_center"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M16" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td><td class="align_center"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M17" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td></tr><tr><td class="align_left">Sample<sub><i>M</i></sub></td><td class="align_center"><i>x</i><sub><i>M</i>1</sub></td><td class="align_center"><i>x</i><sub><i>M</i>2</sub></td><td class="align_center"><span style="width: 15.5623ptpx;"><svg height="4.18388pt" id="M18" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -4.13406 15.5623 4.18388" width="15.5623pt" 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="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.143,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.286,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g></svg></span></td><td class="align_center"><i>x</i><sub><i>MN</i></sub></td><td class="align_center"><span style="width: 16.6542ptpx;"><svg height="9.39034pt" id="M19" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 16.6542 9.39034" width="16.6542pt" 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="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.942,3.132)"><path d="M1006 650H829L492 147L357 650H174L166 618C270 609 275 601 247 502L194 315C158 189 136 127 122 96C104 56 80 37 18 32L12 0H256L263 32C181 40 176 51 183 98C188 132 197 179 226 281L299 541H301L433 6H458L809 551H811L753 141C739 41 734 39 650 32L642 0H917L923 32C836 39 827 41 839 142L887 535C896 610 901 612 997 618L1006 650Z"></path></g></svg></span></td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>A gene expression matrix composed with <i>M</i> samples and <i>N</i> genes.</div>

Computational and Mathematical Methods in Medicine

tab1

Table 1

Table 1: Gene Selection via a New Hybrid Ant Colony Optimization Algorithm for Cancer Classification in High-Dimensional Data 