Multiview Ensemble Method for Detecting Shilling Attacks in Collaborative Recommender Systems

<table class="algorithm-group"><tr><td><table class="algorithm" id="alg3"><tr><td colspan="2">Input: U, I, X, k, d, e, bs, q,Vdata, BsClassifier</td></tr><tr><td colspan="2">Output: TR, Xallopt,Fpre, Vpre</td></tr><tr><td colspan="2">1 TR←<svg height="8.69875pt" id="M128" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 10.7344 8.69875" width="10.7344pt" 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="M683 511L645 549L562 468C514 507 452 530 385 530C231 530 106 407 106 255C106 189 130 128 169 80L87 -1L125 -39L208 42C256 3 318 -20 385 -20C539 -20 664 103 664 255C664 321 640 382 601 430L683 511ZM606 255C606 131 507 30 385 30C332 30 284 49 246 80L561 391C589 353 606 306 606 255ZM524 430L209 119C181 157 164 204 164 255C164 379 263 480 385 480C438 480 486 461 524 430Z" id="g114-170"></path></g></svg>, Fpre←<svg height="8.69875pt" id="M129" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 10.7344 8.69875" width="10.7344pt" 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="M683 511L645 549L562 468C514 507 452 530 385 530C231 530 106 407 106 255C106 189 130 128 169 80L87 -1L125 -39L208 42C256 3 318 -20 385 -20C539 -20 664 103 664 255C664 321 640 382 601 430L683 511ZM606 255C606 131 507 30 385 30C332 30 284 49 246 80L561 391C589 353 606 306 606 255ZM524 430L209 119C181 157 164 204 164 255C164 379 263 480 385 480C438 480 486 461 524 430Z" id="g114-170"></path></g></svg>, Vpre←<svg height="8.69875pt" id="M130" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 10.7344 8.69875" width="10.7344pt" 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="M683 511L645 549L562 468C514 507 452 530 385 530C231 530 106 407 106 255C106 189 130 128 169 80L87 -1L125 -39L208 42C256 3 318 -20 385 -20C539 -20 664 103 664 255C664 321 640 382 601 430L683 511ZM606 255C606 131 507 30 385 30C332 30 284 49 246 80L561 391C589 353 606 306 606 255ZM524 430L209 119C181 157 164 204 164 255C164 379 263 480 385 480C438 480 486 461 524 430Z" id="g114-170"></path></g></svg>, Xallopt←<svg height="8.69875pt" id="M131" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 10.7344 8.69875" width="10.7344pt" 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="M683 511L645 549L562 468C514 507 452 530 385 530C231 530 106 407 106 255C106 189 130 128 169 80L87 -1L125 -39L208 42C256 3 318 -20 385 -20C539 -20 664 103 664 255C664 321 640 382 601 430L683 511ZM606 255C606 131 507 30 385 30C332 30 284 49 246 80L561 391C589 353 606 306 606 255ZM524 430L209 119C181 157 164 204 164 255C164 379 263 480 385 480C438 480 486 461 524 430Z" id="g114-170"></path></g></svg></td></tr><tr><td colspan="2">2 for  p=1 to bs  do</td></tr><tr><td colspan="2">3 Up←selectProfiles(U, d)</td></tr><tr><td colspan="2">4 TRp←getfea(Up)</td></tr><tr><td colspan="2">5 Fprep←getClassfiersPre(Xopt, Vdata, TRp, BsClassifier)</td></tr><tr><td colspan="2">6 Fpre←Fpre∪<svg height="11.5564pt" id="M132" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 12.5481 11.5564" width="12.5481pt" 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="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z" id="g113-124"></path></g><g transform="matrix(.013,0,0,-0.013,4.511,0)"><path d="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z" id="g113-71"></path></g></svg>pr<svg height="14.7625pt" id="M133" style="vertical-align:-5.47417pt" version="1.1" viewbox="-0.0498162 -9.28833 15.9157 14.7625" width="15.9157pt" 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="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z" id="g113-102"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.317,3.132)"><path d="M573 302C573 402 527 451 414 451C386 451 343 446 313 437L330 513L320 522C295 508 261 484 243 463L230 415C194 400 159 383 126 359L131 330C159 344 187 357 222 368L109 -147C96 -204 80 -214 18 -223L13 -255L256 -244L259 -212L236 -210C184 -205 180 -195 191 -141L219 -1C240 -10 268 -12 284 -12C352 4 431 48 484 104C543 166 573 240 573 302ZM481 290C481 165 381 37 305 37C280 37 249 56 235 71L302 395C328 399 353 402 372 402C427 402 481 378 481 290Z" id="g50-113"></path></g><g transform="matrix(.013,0,0,-0.013,11.268,0)"><path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z" id="g113-126"></path></g></svg></td></tr><tr><td colspan="2">7 Vprep←getViewPre(Xopt,Vdata, <svg height="14.2627pt" id="M134" style="vertical-align:-5.30058pt" version="1.1" viewbox="-0.0498162 -8.96212 21.3818 14.2627" width="21.3818pt" 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="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z" id="g113-85"></path></g><g transform="matrix(.013,0,0,-0.013,7.763,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 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</td></tr><tr><td colspan="2">9 Xallopt←Xallopt  <svg height="7.30254pt" id="M136" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -7.25272 7.75925 7.30254" width="7.75925pt" 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="M535 194V548H477V194C477 102 391 35 294 35S111 102 111 194V548H53V194C53 72 166 -15 294 -15S535 72 535 194Z" id="g117-59"></path></g></svg> Xopt</td></tr><tr><td colspan="2">10 if  p mod q=0  then</td></tr><tr><td colspan="2">11 Xopt←constructViews(BsClassfier,X,k,Vdata)</td></tr><tr><td colspan="2">12 end if</td></tr><tr><td colspan="2">13 TR ←TR <svg height="7.30254pt" id="M137" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -7.25272 7.75925 7.30254" width="7.75925pt" 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="M535 194V548H477V194C477 102 391 35 294 35S111 102 111 194V548H53V194C53 72 166 -15 294 -15S535 72 535 194Z" id="g117-59"></path></g></svg> TRp</td></tr><tr><td colspan="2">14 end for</td></tr><tr><td colspan="2">15 return  TR, Xallopt, Fpre, Vpre</td></tr></table></td></tr></table>

<div>The algorithm for training base classifiers.</div>

Security and Communication Networks

alg3

Algorithm 3

Algorithm 3: Multiview Ensemble Method for Detecting Shilling Attacks in Collaborative Recommender Systems 