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type="application/xml" title="MHuiG Blog Site Map" href="https://blog.mhuig.top/sitemap.xml"><link rel="author" href="https://mhuig.top"><meta name="author" content="MHuiG"><meta name="creator" content="MHuiG"><link rel="archives" href="https://blog.mhuig.top/archives/"><link rel="preload" href="/css/style.css" as="style"><link rel="preload" href="https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/fonts/VarelaRound/VarelaRound-Regular.ttf" as="font" type="font/ttf" crossorigin="anonymous"><link rel="preload" href="https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/fonts/VarelaRound/VarelaRound-Regular.ttf" as="font" type="font/ttf" crossorigin="anonymous"><link rel="alternate" href="/atom.xml" title="Magicland" type="application/atom+xml"><link rel="alternate" href="/rss2.xml" title="Magicland" type="application/rss+xml"><title>Spark-快速大数据分析技术: 基于Audioscrobbler数据集的音乐推荐(pyspark) - Magicland</title><meta name="keywords" content="大数据,Spark, BigData,推荐系统,Data mining,ALS算法,音乐推荐系统,隐式反馈数据,ALS协同过滤,音乐推荐系统,PySpark,MHuiG, @MHuiG, Blog, 博客, Magicland, 魔法世界"><meta desc="" name="description" content="本文基于Audioscrobbler数据集（含14.1万用户、160万艺术家及2420万条播放记录），使用PySpark实现ALS协同过滤算法构建音乐推荐系统。通过交替最小二乘法处理隐式反馈数据，将用户-艺术家交互分解为矩阵乘积，设置rank=10、最大迭代15次，最终AUC评估达0.909，衡量推荐质量。 - MHuiG - Magicland"><meta property="og:type" content="website"><meta property="og:title" content="Magicland"><meta property="og:url" content="https://blog.mhuig.top/notes/Spark/als"><meta property="og:site_name" content="Magicland"><meta property="og:description" content="本文基于Audioscrobbler数据集（含14.1万用户、160万艺术家及2420万条播放记录），使用PySpark实现ALS协同过滤算法构建音乐推荐系统。通过交替最小二乘法处理隐式反馈数据，将用户-艺术家交互分解为矩阵乘积，设置rank=10、最大迭代15次，最终AUC评估达0.909，衡量推荐质量。"><meta property="og:locale"><meta property="og:image" content="https://blog.mhuig.top/lib/favicon/android-chrome-192x192.png"><meta property="article:published_time" content="2020-08-02T07:34:00.000Z"><meta property="article:modified_time" 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content="本文基于Audioscrobbler数据集（含14.1万用户、160万艺术家及2420万条播放记录），使用PySpark实现ALS协同过滤算法构建音乐推荐系统。通过交替最小二乘法处理隐式反馈数据，将用户-艺术家交互分解为矩阵乘积，设置rank=10、最大迭代15次，最终AUC评估达0.909，衡量推荐质量。"></span><span hidden=""><meta itemprop="image" content="/lib/favicon/android-chrome-192x192.png"></span><div class="article-meta" id="top"><span hidden="" itemprop="name headline"></span></div><div id="layoutHelper-page-plugins"></div><div id="post-body" itemprop="articleBody"><p> <span class="p logo center large">ALS</span></p><br><h1 hidden="">基于 Audioscrobbler 数据集的音乐推荐 (pyspark)</h1><p>根据用户播放次数数据使用协同过滤算法完成音乐推荐。</p><div class="story post-story"><h2 id="数据集"><a href="#数据集" class="headerlink" title="数据集"></a>数据集</h2><p>Audioscrobbler 数据集</p><span class="btn center large"><a class="button" target="_blank" rel="external nofollow noopener noreferrer" href="/go.html?u=aHR0cDovL3d3dy5pcm8udW1vbnRyZWFsLmNhL35saXNhL2RhdGFzZXRzL3Byb2ZpbGVkYXRhXzA2LU1heS0yMDA1LnRhci5neg" title="下载 Audioscrobbler 数据集"><i class="fas fa-download"></i> 下载 Audioscrobbler 数据集</a></span><h3 id="user-artist-data-txt"><a href="#user-artist-data-txt" class="headerlink" title="user_artist_data.txt"></a><strong>user_artist_data.txt</strong></h3><p>它包含 141000 个用户和 160 万个艺术家，记录了约 2420 万条用户播放艺术家歌曲的信息，其中包括播放次数信息。播放次数较多意味着该用户更喜欢对应艺术家的作品。</p><table><thead><tr><th><strong>userid</strong></th><th><strong>artistid</strong></th><th><strong>playcount</strong></th></tr></thead><tbody><tr><td>用户 ID</td><td>艺术家 ID</td><td>播放次数</td></tr><tr><td>1000002</td><td>1</td><td>55</td></tr></tbody></table><h3 id="artist-data-txt"><a href="#artist-data-txt" class="headerlink" title="artist_data.txt"></a><strong>artist_data.txt</strong></h3><p>该文件包含两列： artistid artist_name 艺术家 ID 艺术家名字。文件中给出了每个艺术家的 ID 和对应的名字。此文件用于 ID 与名字的转换。</p><table><thead><tr><th><strong>artistid</strong></th><th><strong>artist_name</strong></th></tr></thead><tbody><tr><td>艺术家 ID</td><td>艺术家名</td></tr><tr><td>1134999</td><td>06Crazy Life</td></tr></tbody></table><h3 id="artist-alias-txt"><a href="#artist-alias-txt" class="headerlink" title="artist_alias.txt"></a><strong>artist_alias.txt</strong></h3><p>该文件包含两列: badid, goodid 坏 ID 好 ID 。该文件包含已知错误拼写的艺术家 ID 及其对应艺术家的正规的，用于将拼写错误的艺术家 ID 或 ID 变体对应到该艺术家正确的 ID。</p><table><thead><tr><th><strong>badid</strong></th><th><strong>goodid</strong></th></tr></thead><tbody><tr><td>坏 ID</td><td>好 ID</td></tr><tr><td>1092764</td><td>1000311</td></tr></tbody></table></div><div class="story post-story"><h2 id="算法"><a href="#算法" class="headerlink" title="算法"></a>算法</h2><h3 id="交替最小二乘推荐算法-Alternating-Least-Squares，ALS"><a href="#交替最小二乘推荐算法-Alternating-Least-Squares，ALS" class="headerlink" title="交替最小二乘推荐算法 (Alternating Least Squares，ALS)"></a><strong>交替最小二乘推荐算法 (Alternating Least Squares，ALS)</strong></h3><p>人们虽然经常听音乐，但很少给音乐评分。因此 Audioscrobbler 数据集覆盖了更多的用户和艺术家，也包含了更多的总体信息，虽然单条记录的信息比较少。这种类型的数据通常被称为隐式反馈数据，因为用户和艺术家的关系是通过其他行动隐含体现出来的，而不是通过显式的评分或点赞得到的。</p><p>根据两个用户的相似行为判断他们有相同的偏好，学习算法不需要用户和艺术家的属性信息。这类算法通常称为<strong>协同过滤算法</strong>。</p><p><strong>潜在因素模型</strong>：试图通过数据相对少的未被观察到的底层原因，来解释大量用户和产品之间可观察到的交互。因子分析方法背后的理论是，有关观测变量之间的相互依赖性的信息可以稍后用于减少数据集中的变量集。</p><p><strong>矩阵分解模型</strong>：数学上，算法把用户和产品数据当成一个大矩阵 R，矩阵第 i 行和第 j 列上的元素有值，代表用户 i 播放过艺术家 j 的音乐。矩阵 R 是稀疏的：R 中大多数元素都是 0，因为相对于所有可能的用户 - 艺术家组合，只有很少一部分组合会出现在数据中。算法将 R 分解为两个小矩阵 U 和 P 的乘积。矩阵 U 和矩阵 P 非常 “瘦”。因为 A 有很多行和列，但 U 和 P 的行很多而列很少（列数用 k 表示）。这 k 个列就是潜在因素，用于解释数据中的交互关系。由于 k 的值小，矩阵分解算法只能是某种近似。</p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992482915/202082144833.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992482915/202082144833.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="矩阵分解模型"></p><p>为了使低秩矩阵 P 和 U 尽可能的逼近 R，可以通过最小化如下损失函数 L 来完成。</p><p><mjx-container class="MathJax" jax="SVG" 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L(U,P)=\sum_{i,J}(r_{ij}-u_i^TP_j)^2+λ(|u_i|^2+|p_j|^2)^2
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transform="translate(389,0)"></path><path data-c="29" d="M78-245C138-199 188-131 229-40 268 47 288 129 288 208L288 292C288 371 268 453 229 540 188 631 138 699 78 745 75 747 72 748 71 748 62 748 57 743 57 734 57 730 59 726 62 723 114 683 156 617 187 526 214 447 228 369 228 292L228 208C228 131 214 53 187-26 156-117 114-183 62-223 59-227 57-231 57-234 57-243 62-248 71-248 72-248 75-247 78-245Z" transform="translate(889,0)"></path></g></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p>损失函数公式与上图对应：<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.357ex" xmlns="http://www.w3.org/2000/svg" width="2.034ex" height="1.357ex" role="img" focusable="false" viewBox="0 -442 899 599.8"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="u_i"><g data-mml-node="msub" data-latex="u_i"><g data-mml-node="mi" data-latex="u"><path data-c="1D462" d="M543 144C543 153 538 158 527 158 518 158 513 151 510 137 505 118 500 99 493 80 480 39 462 18 440 18 422 18 413 32 413 60 413 77 420 111 433 161L460 267C469 303 477 328 483 359L489 386C491 393 492 398 492 401 492 421 481 431 459 431 437 431 423 419 417 394L343 98C342 95 338 88 330 76 314 50 275 18 235 18 197 18 178 44 178 95 178 136 196 202 231 294 242 324 248 345 248 357 248 407 213 442 163 442 118 442 83 417 58 367 39 328 29 301 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 174 413 181 403 181 384 181 369 175 348 164 319 126 218 107 148 107 111 107 34 155-11 232-11 275-11 314 9 347 50 361 9 391-11 437-11 506-11 527 70 543 144Z"></path></g><g data-mml-node="mi" transform="translate(605,-150) scale(0.707)" data-latex="i"><path data-c="1D456" d="M284 621C284 648 271 661 244 661 216 661 188 633 188 605 188 578 202 565 229 565 257 565 284 593 284 621M259 138C237 59 205 19 164 19 151 19 144 28 144 47 144 64 173 150 232 306 240 329 244 347 244 360 244 409 210 445 161 445 118 445 84 420 59 369 39 328 29 301 29 288 29 279 34 275 45 275 58 275 60 281 64 295 87 375 118 415 158 415 171 415 178 406 178 387 178 373 175 357 168 338 145 275 121 208 101 155 86 115 78 88 78 74 78 25 114-11 162-11 205-11 239 14 264 64 283 103 293 130 293 145 293 154 288 159 277 159 274 159 259 150 259 138Z"></path></g></g></g></g></svg></mjx-container>表示用户 i 的偏好隐含向量，<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.667ex" xmlns="http://www.w3.org/2000/svg" width="1.985ex" height="1.667ex" role="img" focusable="false" viewBox="0 -442 877.3 737"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="p_j"><g data-mml-node="msub" data-latex="p_j"><g data-mml-node="mi" data-latex="p"><path data-c="1D45D" d="M355 442C311 442 269 419 228 373 217 419 186 442 137 442 96 442 66 409 45 344 35 311 30 292 30 286 30 277 35 272 46 272 51 272 54 273 57 275 62 284 65 291 66 298 84 374 107 412 134 412 152 412 161 398 161 371 161 356 159 339 154 321L44-118C35-151 34-155-5-155-23-155-32-163-32-178-32-189-26-194-15-194 0-194 52-191 67-191 86-191 146-194 165-194 180-194 187-186 187-170 187-160 178-155 159-155 141-155 114-156 114-144 114-131 155 26 159 43 179 6 209-13 249-13 314-13 371 20 421 87 467 148 490 213 490 280 490 367 438 442 355 442M352 412C391 412 411 382 411 323 411 296 405 260 394 215 371 128 342 71 307 42 286 25 267 16 248 16 219 16 199 29 188 56 179 77 174 92 174 100L225 309C230 331 248 354 276 377 304 400 329 412 352 412Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)" data-latex="j"><path data-c="1D457" d="M397 621C397 648 383 661 356 661 328 661 300 633 300 605 300 578 313 565 340 565 368 565 397 593 397 621M267 444C214 444 169 404 147 369 120 326 107 299 107 287 107 278 112 274 122 274 127 274 130 275 133 276 138 284 141 291 144 296 176 375 216 414 264 414 282 414 291 400 291 373 291 358 289 341 284 323L192-46C178-104 138-175 75-175 66-175 57-174 48-171 73-161 85-143 85-118 85-92 71-79 44-79 12-79-13-108-13-140-13-184 30-205 77-205 120-205 160-190 197-160 232-131 254-94 265-51L356 311C359 324 361 337 361 349 361 404 322 444 267 444Z"></path></g></g></g></g></svg></mjx-container>表示艺术家 j 包含的隐含特征向量，<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.667ex" xmlns="http://www.w3.org/2000/svg" width="2.419ex" height="1.667ex" role="img" focusable="false" viewBox="0 -442 1069.3 737"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="r_{ij}"><g data-mml-node="msub" data-latex="r_{ij}"><g data-mml-node="mi" data-latex="r"><path data-c="1D45F" d="M436 374C436 416 395 442 351 442 302 442 261 419 227 372 217 411 183 442 136 442 95 442 65 410 44 345 34 312 29 293 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 65 299 83 375 106 413 133 413 150 413 159 399 159 371 159 358 154 331 144 290L87 63C84 50 78 24 78 19 78-1 89-11 110-11 130-11 143-1 150 19L169 91C180 134 187 162 190 175L221 303C223 311 231 324 244 343 271 381 302 413 351 413 363 413 373 411 382 406 352 397 337 378 337 351 337 325 351 312 378 312 411 312 436 341 436 374Z"></path></g><g data-mml-node="TeXAtom" transform="translate(484,-150) scale(0.707)" data-latex="{i j}" data-mjx-texclass="ORD"><g data-mml-node="mi" data-latex="i"><path data-c="1D456" d="M284 621C284 648 271 661 244 661 216 661 188 633 188 605 188 578 202 565 229 565 257 565 284 593 284 621M259 138C237 59 205 19 164 19 151 19 144 28 144 47 144 64 173 150 232 306 240 329 244 347 244 360 244 409 210 445 161 445 118 445 84 420 59 369 39 328 29 301 29 288 29 279 34 275 45 275 58 275 60 281 64 295 87 375 118 415 158 415 171 415 178 406 178 387 178 373 175 357 168 338 145 275 121 208 101 155 86 115 78 88 78 74 78 25 114-11 162-11 205-11 239 14 264 64 283 103 293 130 293 145 293 154 288 159 277 159 274 159 259 150 259 138Z"></path></g><g data-mml-node="mi" data-latex="j" transform="translate(345,0)"><path data-c="1D457" d="M397 621C397 648 383 661 356 661 328 661 300 633 300 605 300 578 313 565 340 565 368 565 397 593 397 621M267 444C214 444 169 404 147 369 120 326 107 299 107 287 107 278 112 274 122 274 127 274 130 275 133 276 138 284 141 291 144 296 176 375 216 414 264 414 282 414 291 400 291 373 291 358 289 341 284 323L192-46C178-104 138-175 75-175 66-175 57-174 48-171 73-161 85-143 85-118 85-92 71-79 44-79 12-79-13-108-13-140-13-184 30-205 77-205 120-205 160-190 197-160 232-131 254-94 265-51L356 311C359 324 361 337 361 349 361 404 322 444 267 444Z"></path></g></g></g></g></g></svg></mjx-container>表示用户 i 对艺术家 j 的评分，<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.667ex" xmlns="http://www.w3.org/2000/svg" width="4.908ex" height="2.572ex" role="img" focusable="false" viewBox="0 -841.7 2169.1 1136.7"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="u_i^TP_j"><g data-mml-node="msubsup" data-latex="u_i^T"><g data-mml-node="mi" data-latex="u"><path data-c="1D462" d="M543 144C543 153 538 158 527 158 518 158 513 151 510 137 505 118 500 99 493 80 480 39 462 18 440 18 422 18 413 32 413 60 413 77 420 111 433 161L460 267C469 303 477 328 483 359L489 386C491 393 492 398 492 401 492 421 481 431 459 431 437 431 423 419 417 394L343 98C342 95 338 88 330 76 314 50 275 18 235 18 197 18 178 44 178 95 178 136 196 202 231 294 242 324 248 345 248 357 248 407 213 442 163 442 118 442 83 417 58 367 39 328 29 301 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 174 413 181 403 181 384 181 369 175 348 164 319 126 218 107 148 107 111 107 34 155-11 232-11 275-11 314 9 347 50 361 9 391-11 437-11 506-11 527 70 543 144Z"></path></g><g data-mml-node="mi" transform="translate(605,363) scale(0.707)" data-latex="T"><path data-c="1D447" d="M344 631C344 628 343 621 340 611L208 83C204 68 200 59 197 55 188 44 154 39 94 39 63 39 49 42 49 16 49 5 56 0 69 0 120 0 192 4 235 3L317 2C331 2 386 0 403 0 420 0 428 8 428 24 428 34 416 39 391 39 339 39 309 41 300 46 297 48 295 52 295 58L430 603C433 617 436 626 439 629 443 635 467 638 511 638 566 638 604 634 623 625 642 616 652 595 652 561 652 543 649 517 644 483 642 475 641 469 641 464 641 453 646 447 657 447 666 447 672 456 675 473L702 645C703 650 704 656 704 662 704 672 694 677 673 677L125 677C99 677 97 674 89 655L30 481C27 472 25 466 24 462 24 452 29 447 40 447 48 447 55 455 60 470 85 543 110 588 133 607 159 628 209 638 282 638L321 638C332 638 344 639 344 631Z"></path></g><g data-mml-node="mi" transform="translate(605,-284.4) scale(0.707)" data-latex="i"><path data-c="1D456" d="M284 621C284 648 271 661 244 661 216 661 188 633 188 605 188 578 202 565 229 565 257 565 284 593 284 621M259 138C237 59 205 19 164 19 151 19 144 28 144 47 144 64 173 150 232 306 240 329 244 347 244 360 244 409 210 445 161 445 118 445 84 420 59 369 39 328 29 301 29 288 29 279 34 275 45 275 58 275 60 281 64 295 87 375 118 415 158 415 171 415 178 406 178 387 178 373 175 357 168 338 145 275 121 208 101 155 86 115 78 88 78 74 78 25 114-11 162-11 205-11 239 14 264 64 283 103 293 130 293 145 293 154 288 159 277 159 274 159 259 150 259 138Z"></path></g></g><g data-mml-node="msub" data-latex="P_j" transform="translate(1152.8,0)"><g data-mml-node="mi" data-latex="P"><path data-c="1D443" d="M555 683 235 683C212 683 201 682 201 660 201 649 212 644 234 644 254 644 294 647 294 631 294 629 293 623 290 613L158 82C152 60 142 47 128 42 121 40 103 39 72 39 50 39 40 37 40 16 40 5 46 0 59 0L184 3 248 2C259 2 299 0 312 0 328 0 336 8 336 24 336 34 325 39 304 39 264 39 244 43 244 52 244 52 245 55 247 68L307 312 472 312C537 312 599 332 657 371 722 414 754 467 754 530 754 629 660 683 555 683M524 644C611 644 654 614 654 554 654 498 626 423 597 397 559 363 509 346 447 346L313 346 379 610C387 644 387 644 429 644Z"></path></g><g data-mml-node="mi" transform="translate(675,-150) scale(0.707)" data-latex="j"><path data-c="1D457" d="M397 621C397 648 383 661 356 661 328 661 300 633 300 605 300 578 313 565 340 565 368 565 397 593 397 621M267 444C214 444 169 404 147 369 120 326 107 299 107 287 107 278 112 274 122 274 127 274 130 275 133 276 138 284 141 291 144 296 176 375 216 414 264 414 282 414 291 400 291 373 291 358 289 341 284 323L192-46C178-104 138-175 75-175 66-175 57-174 48-171 73-161 85-143 85-118 85-92 71-79 44-79 12-79-13-108-13-140-13-184 30-205 77-205 120-205 160-190 197-160 232-131 254-94 265-51L356 311C359 324 361 337 361 349 361 404 322 444 267 444Z"></path></g></g></g></g></svg></mjx-container>是用户 i 对艺术家 j 评分的近似。其中 λ 是正则化项的系数，损失函数一般需要加入正则化项来避免过拟合等问题。</p><p>于是就简化为一个最小化损失函数 L 的优化问题。用户 - 特征矩阵<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.719ex" height="1.595ex" role="img" focusable="false" viewBox="0 -683 760 705"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="U"><g data-mml-node="mi" data-latex="U"><path data-c="1D448" d="M642 680C623 680 559 683 540 683 525 683 518 675 518 659 518 650 525 645 539 644 582 644 603 631 603 605 603 599 602 592 600 585L511 232C496 175 467 126 424 84 377 39 325 17 269 17 195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641 292 643 309 644 338 644 364 644 375 644 375 668 375 678 369 683 358 683L231 680 104 683C88 683 81 674 81 659 81 652 84 647 89 646 99 645 107 644 112 644 143 643 161 641 166 640 171 639 173 636 173 631 173 629 172 622 169 611L74 230C69 211 67 192 67 172 67 57 150-22 265-22 330-22 390 3 445 54 498 102 532 158 548 223L636 574C649 625 677 643 739 644 753 645 760 653 760 668L760 672C757 679 752 683 743 683 724 683 661 680 642 680Z"></path></g></g></g></svg></mjx-container>和特征 - 艺术家矩阵<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.706ex" height="1.545ex" role="img" focusable="false" viewBox="0 -683 754 683"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="P"><g data-mml-node="mi" data-latex="P"><path data-c="1D443" d="M555 683 235 683C212 683 201 682 201 660 201 649 212 644 234 644 254 644 294 647 294 631 294 629 293 623 290 613L158 82C152 60 142 47 128 42 121 40 103 39 72 39 50 39 40 37 40 16 40 5 46 0 59 0L184 3 248 2C259 2 299 0 312 0 328 0 336 8 336 24 336 34 325 39 304 39 264 39 244 43 244 52 244 52 245 55 247 68L307 312 472 312C537 312 599 332 657 371 722 414 754 467 754 530 754 629 660 683 555 683M524 644C611 644 654 614 654 554 654 498 626 423 597 397 559 363 509 346 447 346L313 346 379 610C387 644 387 644 429 644Z"></path></g></g></g></svg></mjx-container>的乘积的结果是对整个稠密的用户 - 艺术家相互关系矩阵<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="4.865ex" height="1.954ex" role="img" focusable="false" viewBox="0 -841.7 2150.4 863.7"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="UP^T"><g data-mml-node="mi" data-latex="U"><path data-c="1D448" d="M642 680C623 680 559 683 540 683 525 683 518 675 518 659 518 650 525 645 539 644 582 644 603 631 603 605 603 599 602 592 600 585L511 232C496 175 467 126 424 84 377 39 325 17 269 17 195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641 292 643 309 644 338 644 364 644 375 644 375 668 375 678 369 683 358 683L231 680 104 683C88 683 81 674 81 659 81 652 84 647 89 646 99 645 107 644 112 644 143 643 161 641 166 640 171 639 173 636 173 631 173 629 172 622 169 611L74 230C69 211 67 192 67 172 67 57 150-22 265-22 330-22 390 3 445 54 498 102 532 158 548 223L636 574C649 625 677 643 739 644 753 645 760 653 760 668L760 672C757 679 752 683 743 683 724 683 661 680 642 680Z"></path></g><g data-mml-node="msup" data-latex="P^T" transform="translate(760,0)"><g data-mml-node="mi" data-latex="P"><path data-c="1D443" d="M555 683 235 683C212 683 201 682 201 660 201 649 212 644 234 644 254 644 294 647 294 631 294 629 293 623 290 613L158 82C152 60 142 47 128 42 121 40 103 39 72 39 50 39 40 37 40 16 40 5 46 0 59 0L184 3 248 2C259 2 299 0 312 0 328 0 336 8 336 24 336 34 325 39 304 39 264 39 244 43 244 52 244 52 245 55 247 68L307 312 472 312C537 312 599 332 657 371 722 414 754 467 754 530 754 629 660 683 555 683M524 644C611 644 654 614 654 554 654 498 626 423 597 397 559 363 509 346 447 346L313 346 379 610C387 644 387 644 429 644Z"></path></g><g data-mml-node="mi" transform="translate(842.6,363) scale(0.707)" data-latex="T"><path data-c="1D447" d="M344 631C344 628 343 621 340 611L208 83C204 68 200 59 197 55 188 44 154 39 94 39 63 39 49 42 49 16 49 5 56 0 69 0 120 0 192 4 235 3L317 2C331 2 386 0 403 0 420 0 428 8 428 24 428 34 416 39 391 39 339 39 309 41 300 46 297 48 295 52 295 58L430 603C433 617 436 626 439 629 443 635 467 638 511 638 566 638 604 634 623 625 642 616 652 595 652 561 652 543 649 517 644 483 642 475 641 469 641 464 641 453 646 447 657 447 666 447 672 456 675 473L702 645C703 650 704 656 704 662 704 672 694 677 673 677L125 677C99 677 97 674 89 655L30 481C27 472 25 466 24 462 24 452 29 447 40 447 48 447 55 455 60 470 85 543 110 588 133 607 159 628 209 638 282 638L321 638C332 638 344 639 344 631Z"></path></g></g></g></g></svg></mjx-container>的完整估计。该乘积可以理解成艺术家与其属性之间的一个映射，然后按用户属性进行加权。</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="1.717ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 759 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="R=UP^T"><g data-mml-node="mi" data-latex="R"><path data-c="1D445" d="M739 531C739 582 713 621 662 649 621 672 572 683 517 683L235 683C212 683 202 682 202 659 202 652 205 647 211 646 221 645 229 644 234 644 264 643 281 641 286 640 291 639 294 636 294 631 294 629 293 623 290 613L158 82C153 60 143 46 128 41 121 39 103 38 72 38 50 38 41 37 41 15 41 4 47-1 59 0L183 3 309 0C325-1 333 8 333 23 333 33 322 38 301 38 261 38 241 43 241 52 241 52 242 54 244 68L308 327 423 327C492 327 527 298 527 241 527 232 522 210 513 174 502 132 497 104 497 89 497 13 556-22 632-22 660-22 687-9 714 16 741 41 755 68 755 96 755 106 750 111 739 111 732 111 726 106 723 95 712 64 698 41 682 28 666 15 651 8 636 8 613 8 601 27 601 64 601 88 604 125 611 176 614 197 615 212 615 223 615 276 587 315 531 339 625 362 739 429 739 531M609 616C629 603 639 581 639 550 639 530 635 507 626 480 599 398 531 357 422 357L316 357 379 610C384 631 392 642 403 643 408 644 428 644 463 644 528 644 566 642 609 616Z"></path></g></g></g></svg><mjx-break size="4"></mjx-break><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="7.254ex" height="2.47ex" role="img" focusable="false" viewBox="0 -841.7 3206.2 1091.7"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="R=UP^T"><g data-mml-node="mo" data-latex="="><path data-c="3D" d="M698 367 80 367C64 367 56 359 56 344 56 329 64 321 80 321L698 321C714 321 722 329 722 344 722 356 711 367 698 367M698 179 80 179C64 179 56 171 56 156 56 141 64 133 80 133L698 133C714 133 722 141 722 156 722 169 711 179 698 179Z"></path></g><g data-mml-node="mi" data-latex="U" transform="translate(1055.8,0)"><path data-c="1D448" d="M642 680C623 680 559 683 540 683 525 683 518 675 518 659 518 650 525 645 539 644 582 644 603 631 603 605 603 599 602 592 600 585L511 232C496 175 467 126 424 84 377 39 325 17 269 17 195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641 292 643 309 644 338 644 364 644 375 644 375 668 375 678 369 683 358 683L231 680 104 683C88 683 81 674 81 659 81 652 84 647 89 646 99 645 107 644 112 644 143 643 161 641 166 640 171 639 173 636 173 631 173 629 172 622 169 611L74 230C69 211 67 192 67 172 67 57 150-22 265-22 330-22 390 3 445 54 498 102 532 158 548 223L636 574C649 625 677 643 739 644 753 645 760 653 760 668L760 672C757 679 752 683 743 683 724 683 661 680 642 680Z"></path></g><g data-mml-node="msup" data-latex="P^T" transform="translate(1815.8,0)"><g data-mml-node="mi" data-latex="P"><path data-c="1D443" d="M555 683 235 683C212 683 201 682 201 660 201 649 212 644 234 644 254 644 294 647 294 631 294 629 293 623 290 613L158 82C152 60 142 47 128 42 121 40 103 39 72 39 50 39 40 37 40 16 40 5 46 0 59 0L184 3 248 2C259 2 299 0 312 0 328 0 336 8 336 24 336 34 325 39 304 39 264 39 244 43 244 52 244 52 245 55 247 68L307 312 472 312C537 312 599 332 657 371 722 414 754 467 754 530 754 629 660 683 555 683M524 644C611 644 654 614 654 554 654 498 626 423 597 397 559 363 509 346 447 346L313 346 379 610C387 644 387 644 429 644Z"></path></g><g data-mml-node="mi" transform="translate(842.6,363) scale(0.707)" data-latex="T"><path data-c="1D447" d="M344 631C344 628 343 621 340 611L208 83C204 68 200 59 197 55 188 44 154 39 94 39 63 39 49 42 49 16 49 5 56 0 69 0 120 0 192 4 235 3L317 2C331 2 386 0 403 0 420 0 428 8 428 24 428 34 416 39 391 39 339 39 309 41 300 46 297 48 295 52 295 58L430 603C433 617 436 626 439 629 443 635 467 638 511 638 566 638 604 634 623 625 642 616 652 595 652 561 652 543 649 517 644 483 642 475 641 469 641 464 641 453 646 447 657 447 666 447 672 456 675 473L702 645C703 650 704 656 704 662 704 672 694 677 673 677L125 677C99 677 97 674 89 655L30 481C27 472 25 466 24 462 24 452 29 447 40 447 48 447 55 455 60 470 85 543 110 588 133 607 159 628 209 638 282 638L321 638C332 638 344 639 344 631Z"></path></g></g></g></g></svg></mjx-container>通常没有确切的解，因为 U 和 P 通常不够大，不足以完全表示 R，<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="4.865ex" height="1.954ex" role="img" focusable="false" viewBox="0 -841.7 2150.4 863.7"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="UP^T"><g data-mml-node="mi" data-latex="U"><path data-c="1D448" d="M642 680C623 680 559 683 540 683 525 683 518 675 518 659 518 650 525 645 539 644 582 644 603 631 603 605 603 599 602 592 600 585L511 232C496 175 467 126 424 84 377 39 325 17 269 17 195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641 292 643 309 644 338 644 364 644 375 644 375 668 375 678 369 683 358 683L231 680 104 683C88 683 81 674 81 659 81 652 84 647 89 646 99 645 107 644 112 644 143 643 161 641 166 640 171 639 173 636 173 631 173 629 172 622 169 611L74 230C69 211 67 192 67 172 67 57 150-22 265-22 330-22 390 3 445 54 498 102 532 158 548 223L636 574C649 625 677 643 739 644 753 645 760 653 760 668L760 672C757 679 752 683 743 683 724 683 661 680 642 680Z"></path></g><g data-mml-node="msup" data-latex="P^T" transform="translate(760,0)"><g data-mml-node="mi" data-latex="P"><path data-c="1D443" d="M555 683 235 683C212 683 201 682 201 660 201 649 212 644 234 644 254 644 294 647 294 631 294 629 293 623 290 613L158 82C152 60 142 47 128 42 121 40 103 39 72 39 50 39 40 37 40 16 40 5 46 0 59 0L184 3 248 2C259 2 299 0 312 0 328 0 336 8 336 24 336 34 325 39 304 39 264 39 244 43 244 52 244 52 245 55 247 68L307 312 472 312C537 312 599 332 657 371 722 414 754 467 754 530 754 629 660 683 555 683M524 644C611 644 654 614 654 554 654 498 626 423 597 397 559 363 509 346 447 346L313 346 379 610C387 644 387 644 429 644Z"></path></g><g data-mml-node="mi" transform="translate(842.6,363) scale(0.707)" data-latex="T"><path data-c="1D447" d="M344 631C344 628 343 621 340 611L208 83C204 68 200 59 197 55 188 44 154 39 94 39 63 39 49 42 49 16 49 5 56 0 69 0 120 0 192 4 235 3L317 2C331 2 386 0 403 0 420 0 428 8 428 24 428 34 416 39 391 39 339 39 309 41 300 46 297 48 295 52 295 58L430 603C433 617 436 626 439 629 443 635 467 638 511 638 566 638 604 634 623 625 642 616 652 595 652 561 652 543 649 517 644 483 642 475 641 469 641 464 641 453 646 447 657 447 666 447 672 456 675 473L702 645C703 650 704 656 704 662 704 672 694 677 673 677L125 677C99 677 97 674 89 655L30 481C27 472 25 466 24 462 24 452 29 447 40 447 48 447 55 455 60 470 85 543 110 588 133 607 159 628 209 638 282 638L321 638C332 638 344 639 344 631Z"></path></g></g></g></g></svg></mjx-container>应该尽可能逼近 R。然而不幸的是，想直接同时得到 U 和 P 的最优解是不可能的。</p><p>如果 P 已知，求 U 的最优解是非常容易的，反之亦然。但 P 和 U 事先都是未知的。</p><p>虽然 P 是未知的，但可以把 P 初始化为随机行向量矩阵。接着运用简单的线性代数，就能在给定 R 和 P 的条件下求出 U 的最优解。实际上，U 的第 i 行是 R 的第 i 行和 P 的函数。</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:27.712ex"><svg style="vertical-align:-.726ex;min-width:27.712ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.583ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -820.9)"><g data-mml-node="math" data-latex="
R_iP(P^TP)^{-1}=U_i
"><g data-mml-node="mtable" data-latex="
R_iP(P^TP)^{-1}=U_i
" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 820.9) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="4046.3 -820.9 1 1141.7"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" transform="translate(0,-70.9)"><g data-mml-node="mtd"><g data-mml-node="msub" data-latex="R_i"><g data-mml-node="mi" data-latex="R"><path data-c="1D445" d="M739 531C739 582 713 621 662 649 621 672 572 683 517 683L235 683C212 683 202 682 202 659 202 652 205 647 211 646 221 645 229 644 234 644 264 643 281 641 286 640 291 639 294 636 294 631 294 629 293 623 290 613L158 82C153 60 143 46 128 41 121 39 103 38 72 38 50 38 41 37 41 15 41 4 47-1 59 0L183 3 309 0C325-1 333 8 333 23 333 33 322 38 301 38 261 38 241 43 241 52 241 52 242 54 244 68L308 327 423 327C492 327 527 298 527 241 527 232 522 210 513 174 502 132 497 104 497 89 497 13 556-22 632-22 660-22 687-9 714 16 741 41 755 68 755 96 755 106 750 111 739 111 732 111 726 106 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138Z"></path></g></g><g data-mml-node="mi" data-latex="P" transform="translate(1086,0)"><path data-c="1D443" d="M555 683 235 683C212 683 201 682 201 660 201 649 212 644 234 644 254 644 294 647 294 631 294 629 293 623 290 613L158 82C152 60 142 47 128 42 121 40 103 39 72 39 50 39 40 37 40 16 40 5 46 0 59 0L184 3 248 2C259 2 299 0 312 0 328 0 336 8 336 24 336 34 325 39 304 39 264 39 244 43 244 52 244 52 245 55 247 68L307 312 472 312C537 312 599 332 657 371 722 414 754 467 754 530 754 629 660 683 555 683M524 644C611 644 654 614 654 554 654 498 626 423 597 397 559 363 509 346 447 346L313 346 379 610C387 644 387 644 429 644Z"></path></g><g data-mml-node="mo" data-latex="(" transform="translate(1840,0)"><path data-c="28" d="M318-248C327-248 332-243 332-234 332-231 330-227 327-223 275-183 233-117 202-26 175 53 161 131 161 208L161 292C161 369 175 447 202 526 233 617 275 683 327 723 330 726 332 730 332 734 332 743 327 748 318 748 317 748 314 747 311 745 251 699 201 631 160 540 121 453 101 371 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2C331 2 386 0 403 0 420 0 428 8 428 24 428 34 416 39 391 39 339 39 309 41 300 46 297 48 295 52 295 58L430 603C433 617 436 626 439 629 443 635 467 638 511 638 566 638 604 634 623 625 642 616 652 595 652 561 652 543 649 517 644 483 642 475 641 469 641 464 641 453 646 447 657 447 666 447 672 456 675 473L702 645C703 650 704 656 704 662 704 672 694 677 673 677L125 677C99 677 97 674 89 655L30 481C27 472 25 466 24 462 24 452 29 447 40 447 48 447 55 455 60 470 85 543 110 588 133 607 159 628 209 638 282 638L321 638C332 638 344 639 344 631Z"></path></g></g><g data-mml-node="mi" data-latex="P" transform="translate(3619.4,0)"><path data-c="1D443" d="M555 683 235 683C212 683 201 682 201 660 201 649 212 644 234 644 254 644 294 647 294 631 294 629 293 623 290 613L158 82C152 60 142 47 128 42 121 40 103 39 72 39 50 39 40 37 40 16 40 5 46 0 59 0L184 3 248 2C259 2 299 0 312 0 328 0 336 8 336 24 336 34 325 39 304 39 264 39 244 43 244 52 244 52 245 55 247 68L307 312 472 312C537 312 599 332 657 371 722 414 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156 191 163 217L259 602C264 623 273 636 286 641 292 643 309 644 338 644 364 644 375 644 375 668 375 678 369 683 358 683L231 680 104 683C88 683 81 674 81 659 81 652 84 647 89 646 99 645 107 644 112 644 143 643 161 641 166 640 171 639 173 636 173 631 173 629 172 622 169 611L74 230C69 211 67 192 67 172 67 57 150-22 265-22 330-22 390 3 445 54 498 102 532 158 548 223L636 574C649 625 677 643 739 644 753 645 760 653 760 668L760 672C757 679 752 683 743 683 724 683 661 680 642 680Z"></path></g><g data-mml-node="mi" transform="translate(716,-150) scale(0.707)" data-latex="i"><path data-c="1D456" d="M284 621C284 648 271 661 244 661 216 661 188 633 188 605 188 578 202 565 229 565 257 565 284 593 284 621M259 138C237 59 205 19 164 19 151 19 144 28 144 47 144 64 173 150 232 306 240 329 244 347 244 360 244 409 210 445 161 445 118 445 84 420 59 369 39 328 29 301 29 288 29 279 34 275 45 275 58 275 60 281 64 295 87 375 118 415 158 415 171 415 178 406 178 387 178 373 175 357 168 338 145 275 121 208 101 155 86 115 78 88 78 74 78 25 114-11 162-11 205-11 239 14 264 64 283 103 293 130 293 145 293 154 288 159 277 159 274 159 259 150 259 138Z"></path></g></g></g></g></g></svg><svg data-labels="true" preserveAspectRatio="xMaxYMid" viewBox="1278 -820.9 1 1141.7"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:2" transform="translate(0,677.1)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(2)}"><path data-c="28" d="M318-248C327-248 332-243 332-234 332-231 330-227 327-223 275-183 233-117 202-26 175 53 161 131 161 208L161 292C161 369 175 447 202 526 233 617 275 683 327 723 330 726 332 730 332 734 332 743 327 748 318 748 317 748 314 747 311 745 251 699 201 631 160 540 121 453 101 371 101 292L101 208C101 129 121 47 160-40 201-131 251-199 311-245 314-247 317-248 318-248Z"></path><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z" transform="translate(389,0)"></path><path data-c="29" d="M78-245C138-199 188-131 229-40 268 47 288 129 288 208L288 292C288 371 268 453 229 540 188 631 138 699 78 745 75 747 72 748 71 748 62 748 57 743 57 734 57 730 59 726 62 723 114 683 156 617 187 526 214 447 228 369 228 292L228 208C228 131 214 53 187-26 156-117 114-183 62-223 59-227 57-231 57-234 57-243 62-248 71-248 72-248 75-247 78-245Z" transform="translate(889,0)"></path></g></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p>因此可以很容易分开计算 U 的每一行。因为 U 的每一行可以分开计算，所以我们可以将其并行化，而并行化是大规模计算的一大优点。</p><p>ALS 是求解<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.561ex" xmlns="http://www.w3.org/2000/svg" width="6.739ex" height="2.253ex" role="img" focusable="false" viewBox="0 -748 2978.7 996"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="L(u,p)"><g data-mml-node="mi" data-latex="L"><path data-c="1D43F" d="M520 667C520 678 513 683 500 683L354 680 223 683C208 684 200 676 200 659 200 652 203 647 209 646 218 645 226 644 231 644 262 643 279 641 284 640 289 639 292 636 292 631 292 629 291 623 288 613L156 82C150 60 140 47 125 42 119 40 101 39 70 39 49 39 39 31 39 15 39 5 49 0 70 0L527 0C552 0 554 0 561 19L639 233C642 240 643 245 643 248 643 258 638 263 627 263 617 263 612 254 607 240 588 191 570 154 555 131 518 75 455 39 363 39L270 39C259 39 252 39 249 40 242 40 239 42 239 45 239 47 241 54 244 67L377 601C383 624 396 637 415 642 421 643 442 644 478 644 506 644 520 644 520 667Z"></path></g><g data-mml-node="mo" data-latex="(" transform="translate(681,0)"><path data-c="28" d="M318-248C327-248 332-243 332-234 332-231 330-227 327-223 275-183 233-117 202-26 175 53 161 131 161 208L161 292C161 369 175 447 202 526 233 617 275 683 327 723 330 726 332 730 332 734 332 743 327 748 318 748 317 748 314 747 311 745 251 699 201 631 160 540 121 453 101 371 101 292L101 208C101 129 121 47 160-40 201-131 251-199 311-245 314-247 317-248 318-248Z"></path></g><g data-mml-node="mi" data-latex="u" transform="translate(1070,0)"><path data-c="1D462" d="M543 144C543 153 538 158 527 158 518 158 513 151 510 137 505 118 500 99 493 80 480 39 462 18 440 18 422 18 413 32 413 60 413 77 420 111 433 161L460 267C469 303 477 328 483 359L489 386C491 393 492 398 492 401 492 421 481 431 459 431 437 431 423 419 417 394L343 98C342 95 338 88 330 76 314 50 275 18 235 18 197 18 178 44 178 95 178 136 196 202 231 294 242 324 248 345 248 357 248 407 213 442 163 442 118 442 83 417 58 367 39 328 29 301 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 174 413 181 403 181 384 181 369 175 348 164 319 126 218 107 148 107 111 107 34 155-11 232-11 275-11 314 9 347 50 361 9 391-11 437-11 506-11 527 70 543 144Z"></path></g><g data-mml-node="mo" data-latex="," transform="translate(1642,0)"><path data-c="2C" d="M139 106C107 106 86 82 86 50 86 20 109-5 139-5 153-5 165-1 174 8L175 0C175-63 154-117 112-160 105-168 101-174 101-178 101-188 105-193 114-193 123-193 135-181 152-158 186-110 203-57 203 0 203 53 185 106 139 106Z"></path></g><g data-mml-node="mi" data-latex="p" transform="translate(2086.7,0)"><path data-c="1D45D" d="M355 442C311 442 269 419 228 373 217 419 186 442 137 442 96 442 66 409 45 344 35 311 30 292 30 286 30 277 35 272 46 272 51 272 54 273 57 275 62 284 65 291 66 298 84 374 107 412 134 412 152 412 161 398 161 371 161 356 159 339 154 321L44-118C35-151 34-155-5-155-23-155-32-163-32-178-32-189-26-194-15-194 0-194 52-191 67-191 86-191 146-194 165-194 180-194 187-186 187-170 187-160 178-155 159-155 141-155 114-156 114-144 114-131 155 26 159 43 179 6 209-13 249-13 314-13 371 20 421 87 467 148 490 213 490 280 490 367 438 442 355 442M352 412C391 412 411 382 411 323 411 296 405 260 394 215 371 128 342 71 307 42 286 25 267 16 248 16 219 16 199 29 188 56 179 77 174 92 174 100L225 309C230 331 248 354 276 377 304 400 329 412 352 412Z"></path></g><g data-mml-node="mo" data-latex=")" transform="translate(2589.7,0)"><path data-c="29" d="M78-245C138-199 188-131 229-40 268 47 288 129 288 208L288 292C288 371 268 453 229 540 188 631 138 699 78 745 75 747 72 748 71 748 62 748 57 743 57 734 57 730 59 726 62 723 114 683 156 617 187 526 214 447 228 369 228 292L228 208C228 131 214 53 187-26 156-117 114-183 62-223 59-227 57-231 57-234 57-243 62-248 71-248 72-248 75-247 78-245Z"></path></g></g></g></svg></mjx-container>的著名算法，固定 P 或 U 对其对应的隐含向量求偏导数并令导数为 0，得到求解公式：</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:33.413ex"><svg style="vertical-align:-.726ex;min-width:33.413ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.583ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -820.9)"><g data-mml-node="math" data-latex="
u_i=(P^TP+λI)^{-1}P^Tr_i
"><g data-mml-node="mtable" data-latex="
u_i=(P^TP+λI)^{-1}P^Tr_i
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transform="translate(889,0)"></path></g></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p>随机对 P、Q 初始化，随后交替进行优化直到收敛。收敛标准是均方误差小于预定义阈值，或者到达最大迭代次数。</p><h3 id="推荐质量评价指标AUC"><a href="#推荐质量评价指标AUC" class="headerlink" title="推荐质量评价指标AUC"></a><strong>推荐质量评价指标 AUC</strong></h3><p>AUC 指标是一个 [0,1] 之间的实数，代表如果随机挑选一个正样本和一个负样本，分类算法将这个正样本排在负样本前面的概率。值越大，表示分类算法更有可能将正样本排在前面，也即算法准确性越好。</p><p>随机抽出一对样本（一个正样本，一个负样本），然后用训练得到的分类器来对这两个样本进行预测，预测得到正样本的概率大于负样本概率的概率。<br><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:36.918ex"><svg style="vertical-align:-.643ex;min-width:36.918ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.417ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -784.1)"><g data-mml-node="math" data-latex="
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data-mml-node="mtext" data-latex="\text{(6)}"><path data-c="28" d="M318-248C327-248 332-243 332-234 332-231 330-227 327-223 275-183 233-117 202-26 175 53 161 131 161 208L161 292C161 369 175 447 202 526 233 617 275 683 327 723 330 726 332 730 332 734 332 743 327 748 318 748 317 748 314 747 311 745 251 699 201 631 160 540 121 453 101 371 101 292L101 208C101 129 121 47 160-40 201-131 251-199 311-245 314-247 317-248 318-248Z"></path><path data-c="36" d="M383 504C416 504 432 521 432 555 432 627 378 666 304 666 221 666 155 627 106 548 63 480 42 403 42 316 42 189 65 100 112 47 152 1 198-22 251-22 312-22 362 1 401 47 438 91 457 144 457 205 457 266 439 318 403 361 365 407 316 431 257 431 205 431 165 402 138 346L138 352C138 465 166 561 226 605 252 624 279 633 306 633 342 633 368 623 385 602 351 602 334 583 334 553 334 525 355 504 383 504M344 340C355 317 361 272 361 206 361 141 356 98 345 76 325 35 294 14 251 14 222 14 200 24 184 44 171 60 162 74 158 85 146 116 140 163 140 227 140 255 144 282 151 308 164 355 201 399 256 399 295 399 325 379 344 340Z" transform="translate(389,0)"></path><path data-c="29" d="M78-245C138-199 188-131 229-40 268 47 288 129 288 208L288 292C288 371 268 453 229 540 188 631 138 699 78 745 75 747 72 748 71 748 62 748 57 743 57 734 57 730 59 726 62 723 114 683 156 617 187 526 214 447 228 369 228 292L228 208C228 131 214 53 187-26 156-117 114-183 62-223 59-227 57-231 57-234 57-243 62-248 71-248 72-248 75-247 78-245Z" transform="translate(889,0)"></path></g></g></g></g></svg></g></g></g></g></svg></mjx-container><br>其中，</p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992541062/202082151944.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992541062/202082151944.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="推荐质量评价指标AUC"></p></div><div class="story post-story"><h2 id="实验过程"><a href="#实验过程" class="headerlink" title="实验过程"></a>实验过程</h2><h3 id="数据预处理"><a href="#数据预处理" class="headerlink" title="数据预处理"></a>数据预处理</h3><p><strong>artist_data.txt</strong> 文件</p><p>数据最终处理成以逗号分割</p><p><strong>artist_data.txt</strong> 文件</p><p>两列之间的间隔有的是空格有的是 Tab，第二列数据中包含空格</p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992773903/202082145015.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992773903/202082145015.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="第二列数据中包含空格"></p><p>因第二列数据中含有逗号和空格，数据最终处理成以 Tab 分割</p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992810226/20208214518.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992810226/20208214518.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="数据最终处理成以Tab分割"></p><p>去除第一列不是数字的行</p><p><strong>artist_alias.txt</strong> <strong>文件</strong></p><p>将拼写错误的艺术家 ID 或 ID 变体对应到该艺术家的规范 ID</p><p>两列之间的间隔有的是空格有的是 Tab</p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992843714/202082145144.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992843714/202082145144.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="两列之间的间隔有的是空格有的是Tab"></p><p>包含数据缺失的列</p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992871540/20208214526.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992871540/20208214526.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="包含数据缺失的列"></p><p>在数据处理时对拼写错误 ID 进行映射，用别名数据集将所有的艺术家 ID 转换成正规 ID。</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">aa={}</span><br><span class="line"><span class="keyword">with</span> <span class="built_in">open</span>(<span class="string">"/export/work/F/1/data/artist_alias.txt"</span>) <span class="keyword">as</span> f:</span><br><span class="line"> line = f.readline()</span><br><span class="line"> <span class="keyword">while</span> line:</span><br><span class="line"> <span class="keyword">if</span> <span class="built_in">len</span>(line.split())==<span class="number">2</span>:</span><br><span class="line"> aa[line.split()[<span class="number">0</span>]]=line.split()[<span class="number">1</span>]</span><br><span class="line"> line = f.readline()</span><br><span class="line"></span><br><span class="line">f3=<span class="built_in">open</span>(<span class="string">"/export/work/F/1/data/user_artist_data.txt.data"</span>,<span class="string">"w+"</span>)</span><br><span class="line"><span class="keyword">with</span> <span class="built_in">open</span>(<span class="string">"/export/work/F/1/data/user_artist_data.txt"</span>) <span class="keyword">as</span> f2:</span><br><span class="line"> line = f2.readline()</span><br><span class="line"> <span class="keyword">while</span> line:</span><br><span class="line"> it=line.split()</span><br><span class="line"> <span class="keyword">if</span> it[<span class="number">1</span>] <span class="keyword">in</span> aa:</span><br><span class="line"> it[<span class="number">1</span>]=aa[it[<span class="number">1</span>]]</span><br><span class="line"> <span class="built_in">print</span>(it[<span class="number">0</span>]+<span class="string">","</span>+it[<span class="number">1</span>]+<span class="string">","</span>+it[<span class="number">2</span>],file=f3)</span><br><span class="line"> line = f2.readline()</span><br><span class="line">f3.close()</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">f5=<span class="built_in">open</span>(<span class="string">"/export/work/F/1/data/artist_data.txt.data"</span>,<span class="string">"w+"</span>)</span><br><span class="line"><span class="keyword">with</span> <span class="built_in">open</span>(<span class="string">"/export/work/F/1/data/artist_data.txt"</span>) <span class="keyword">as</span> f4:</span><br><span class="line"> line = f4.readline()</span><br><span class="line"> <span class="keyword">while</span> line:</span><br><span class="line"> it=line.split()</span><br><span class="line"> s=<span class="string">""</span></span><br><span class="line"> <span class="keyword">for</span> i <span class="keyword">in</span> <span class="built_in">range</span>(<span class="built_in">len</span>(it)):</span><br><span class="line"> s+=it[i]</span><br><span class="line"> <span class="keyword">if</span> i==<span class="number">0</span>:</span><br><span class="line"> s+=<span class="string">" "</span></span><br><span class="line"> <span class="keyword">elif</span> i==<span class="built_in">len</span>(it)-<span class="number">1</span>:</span><br><span class="line"> s+=<span class="string">""</span></span><br><span class="line"> <span class="keyword">else</span>:</span><br><span class="line"> s+=<span class="string">" "</span></span><br><span class="line"> <span class="built_in">print</span>(s,file=f5)</span><br><span class="line"> line = f4.readline()</span><br><span class="line"></span><br><span class="line">f7=<span class="built_in">open</span>(<span class="string">"/export/work/F/1/data/artist_data.txt.data2"</span>,<span class="string">"w+"</span>)</span><br><span class="line"><span class="keyword">with</span> <span class="built_in">open</span>(<span class="string">"/export/work/F/1/data/artist_data.txt.data"</span>) <span class="keyword">as</span> f6:</span><br><span class="line"> line = f6.readline()</span><br><span class="line"> <span class="keyword">while</span> line:</span><br><span class="line"> it=line.split(<span class="string">" "</span>)</span><br><span class="line"> <span class="keyword">try</span>:</span><br><span class="line"> a=<span class="built_in">int</span>(it[<span class="number">0</span>])</span><br><span class="line"> <span class="built_in">print</span>(<span class="built_in">str</span>(a)+<span class="string">" "</span>+it[<span class="number">1</span>],file=f7,end=<span class="string">""</span>)</span><br><span class="line"> <span class="keyword">except</span>:</span><br><span class="line"> <span class="keyword">pass</span></span><br><span class="line"> line = f6.readline()</span><br></pre></td></tr></tbody></table></figure><p><strong>预处理后得到的数据集</strong></p><p><strong>artist_data</strong></p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992906605/202082145243.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992906605/202082145243.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="artist_data"></p><p><strong>user_artist_data</strong></p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992933044/202082145314.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992933044/202082145314.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="user_artist_data"></p><h3 id="获取数据文件，并上传至HDFS"><a href="#获取数据文件，并上传至HDFS" class="headerlink" title="获取数据文件，并上传至HDFS"></a>获取数据文件，并上传至 HDFS</h3><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992959556/202082145341.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992959556/202082145341.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="获取数据文件，并上传至HDFS"></p><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1651992991812/20208214544.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1651992991812/20208214544.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="获取数据文件，并上传至HDFS"></p><h3 id="读入数据，转换成DataFrame备用"><a href="#读入数据，转换成DataFrame备用" class="headerlink" title="读入数据，转换成DataFrame备用"></a>读入数据，转换成 DataFrame 备用</h3><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">from</span> pyspark.sql.types <span class="keyword">import</span> Row</span><br><span class="line"><span class="keyword">from</span> pyspark.sql.types <span class="keyword">import</span> StructType</span><br><span class="line"><span class="keyword">from</span> pyspark.sql.types <span class="keyword">import</span> StructField</span><br><span class="line"><span class="keyword">from</span> pyspark.sql.types <span class="keyword">import</span> StringType,IntegerType</span><br><span class="line"><span class="keyword">from</span> pyspark.conf <span class="keyword">import</span> SparkConf</span><br><span class="line"><span class="keyword">from</span> pyspark <span class="keyword">import</span> SparkContext</span><br><span class="line"><span class="keyword">from</span> pyspark.sql.session <span class="keyword">import</span> SparkSession</span><br><span class="line"><span class="comment"># 转换成DataFrame</span></span><br><span class="line">name1=[<span class="string">"user"</span>, <span class="string">"item"</span>, <span class="string">"rating"</span>]</span><br><span class="line">name2=[<span class="string">"id"</span>,<span class="string">"name"</span>]</span><br><span class="line"></span><br><span class="line">conf = SparkConf().setAppName(<span class="string">"applicaiton"</span>).<span class="built_in">set</span>(<span class="string">"spark.executor.heartbeatInterval"</span>,<span class="string">"500000"</span>).<span class="built_in">set</span>(<span class="string">"spark.network.timeout"</span>,<span class="string">"500000"</span>)</span><br><span class="line">sc = SparkContext.getOrCreate(conf)</span><br><span class="line">spark = SparkSession(sc)</span><br><span class="line">uaRDD = sc.textFile(<span class="string">"/1/user_artist_data.txt.data"</span>)</span><br><span class="line">fields = <span class="built_in">list</span>(<span class="built_in">map</span>( <span class="keyword">lambda</span> fieldName : StructField(fieldName, IntegerType(), nullable = <span class="literal">True</span>), name1))</span><br><span class="line">schema = StructType(fields)</span><br><span class="line">rowRDD = uaRDD.<span class="built_in">map</span>(<span class="keyword">lambda</span> line : line.split(<span class="string">","</span>)).<span class="built_in">map</span>(<span class="keyword">lambda</span> attr : Row(<span class="built_in">int</span>(attr[<span class="number">0</span>]),<span class="built_in">int</span>(attr[<span class="number">1</span>]),<span class="built_in">int</span>(attr[<span class="number">2</span>])))</span><br><span class="line">uaDF = spark.createDataFrame(rowRDD, schema)</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">aRDD = sc.textFile(<span class="string">"/1/artist_data.txt.data2"</span>)</span><br><span class="line">fields = <span class="built_in">list</span>(<span class="built_in">map</span>( <span class="keyword">lambda</span> fieldName : StructField(fieldName, IntegerType(), nullable = <span class="literal">True</span>) <span class="keyword">if</span> fieldName==<span class="string">"id"</span> <span class="keyword">else</span> StructField(fieldName, StringType(), nullable = <span class="literal">True</span>) , name2))</span><br><span class="line">schema = StructType(fields)</span><br><span class="line">rowRDD =aRDD.<span class="built_in">map</span>(<span class="keyword">lambda</span> line : line.split(<span class="string">" "</span>)).<span class="built_in">map</span>(<span class="keyword">lambda</span> attr : Row(<span class="built_in">int</span>(attr[<span class="number">0</span>]),attr[<span class="number">1</span>]))</span><br><span class="line">aDF = spark.createDataFrame(rowRDD, schema)</span><br></pre></td></tr></tbody></table></figure><h3 id="展示数据格式基本统计信息"><a href="#展示数据格式基本统计信息" class="headerlink" title="展示数据格式基本统计信息"></a>展示数据格式基本统计信息</h3><p>数据格式</p><figure class="highlight shell"><table><tbody><tr><td class="code"><pre><span class="line">uaDF.show()</span><br><span class="line"></span><br><span class="line">+-------+-------+------+</span><br><span class="line">| user| item|rating|</span><br><span class="line">+-------+-------+------+</span><br><span class="line">|1000002| 1| 55|</span><br><span class="line">|1000002|1000006| 33|</span><br><span class="line">|1000002|1000007| 8|</span><br><span class="line">|1000002|1000009| 144|</span><br><span class="line">|1000002|1000010| 314|</span><br><span class="line">|1000002|1000013| 8|</span><br><span class="line">|1000002|1000014| 42|</span><br><span class="line">|1000002|1000017| 69|</span><br><span class="line">|1000002|1000024| 329|</span><br><span class="line">|1000002|1000025| 1|</span><br><span class="line">|1000002|1000028| 17|</span><br><span class="line">|1000002|1000031| 47|</span><br><span class="line">|1000002|1000033| 15|</span><br><span class="line">|1000002|1000042| 1|</span><br><span class="line">|1000002|1000045| 1|</span><br><span class="line">|1000002|1000054| 2|</span><br><span class="line">|1000002|1000055| 25|</span><br><span class="line">|1000002|1000056| 4|</span><br><span class="line">|1000002|1000059| 2|</span><br><span class="line">|1000002|1000062| 71|</span><br><span class="line">+-------+-------+------+</span><br><span class="line">only showing top 20 rows</span><br></pre></td></tr></tbody></table></figure><h3 id="基本统计信息"><a href="#基本统计信息" class="headerlink" title="基本统计信息"></a>基本统计信息</h3><p><strong>用户数</strong></p><figure class="highlight shell"><table><tbody><tr><td class="code"><pre><span class="line">a=uaDF.select(uaDF.user).distinct().count()</span><br><span class="line">print(a)</span><br><span class="line"></span><br><span class="line">148111</span><br></pre></td></tr></tbody></table></figure><p><strong>艺术家数目</strong></p><figure class="highlight shell"><table><tbody><tr><td class="code"><pre><span class="line">b=uaDF.select(uaDF.item).distinct().count()</span><br><span class="line">print(b)</span><br><span class="line"></span><br><span class="line">1568126</span><br></pre></td></tr></tbody></table></figure><p><strong>每用户平均播放次数</strong></p><figure class="highlight shell"><table><tbody><tr><td class="code"><pre><span class="line">uaDF.drop("item").groupBy("user").agg({"rating":"mean"}).show()</span><br><span class="line"></span><br><span class="line">+-------+------------------+</span><br><span class="line">| user| avg(rating)|</span><br><span class="line">+-------+------------------+</span><br><span class="line">|1000190|55.355432780847146|</span><br><span class="line">|1001043|6.0131578947368425|</span><br><span class="line">|1001129| 12.32748538011696|</span><br><span class="line">|1001139| 8.652557319223986|</span><br><span class="line">|1002431|12.833333333333334|</span><br><span class="line">|1002605|3.5392670157068062|</span><br><span class="line">|1004666| 9.79409594095941|</span><br><span class="line">|1005158|1.9245283018867925|</span><br><span class="line">|1005439|28.333333333333332|</span><br><span class="line">|1005697|11.733333333333333|</span><br><span class="line">|1005853| 2.5|</span><br><span class="line">|1007007| 2.443396226415094|</span><br><span class="line">|1007847|14.333333333333334|</span><br><span class="line">|1008081|31.232876712328768|</span><br><span class="line">|1008233| 90.0|</span><br><span class="line">|1008804| 9.0|</span><br><span class="line">|1009408| 4.666666666666667|</span><br><span class="line">|1012261|3.2887640449438202|</span><br><span class="line">|1015587| 9.46|</span><br><span class="line">|1016416| 8.241935483870968|</span><br><span class="line">+-------+------------------+</span><br><span class="line">only showing top 20 rows</span><br></pre></td></tr></tbody></table></figure><p><strong>每艺术家平均播放次数</strong></p><figure class="highlight shell"><table><tbody><tr><td class="code"><pre><span class="line">uaDF.drop("user").groupBy("item").agg({"rating":"mean"}).show()</span><br><span class="line"></span><br><span class="line">+-------+------------------+</span><br><span class="line">| item| avg(rating)|</span><br><span class="line">+-------+------------------+</span><br><span class="line">|1001129|10.578309692671395|</span><br><span class="line">|1003373|2.3333333333333335|</span><br><span class="line">|1007972|18.156831042845596|</span><br><span class="line">|1029443| 20.54196642685851|</span><br><span class="line">|1076507| 2.969264544456641|</span><br><span class="line">|1318111|5.6902654867256635|</span><br><span class="line">| 833| 9.483282674772036|</span><br><span class="line">|1239413| 3.821794871794872|</span><br><span class="line">|1000636| 2.0|</span><br><span class="line">|1002431|1.7142857142857142|</span><br><span class="line">|1005697| 3.5|</span><br><span class="line">|1040360| 1.0|</span><br><span class="line">|1043263|1.9166666666666667|</span><br><span class="line">|1245208|19.613390928725703|</span><br><span class="line">| 463| 34.3479262672811|</span><br><span class="line">|1043126|14.580645161290322|</span><br><span class="line">|1001601| 3.573529411764706|</span><br><span class="line">|1091589| 2.5|</span><br><span class="line">|1004021| 6.96403785488959|</span><br><span class="line">|1012885| 4.744927536231884|</span><br><span class="line">+-------+------------------+</span><br><span class="line">only showing top 20 rows</span><br></pre></td></tr></tbody></table></figure><h3 id="构建ALS模型"><a href="#构建ALS模型" class="headerlink" title="构建ALS模型"></a>构建 ALS 模型</h3><p>构建 ALS 模型，并记录所耗时间。初始参数：Rank 10, maxiter 15, RegParm 0.01 Alpha 1.0。</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">from</span> pyspark.ml.recommendation <span class="keyword">import</span> ALS,ALSModel</span><br><span class="line"><span class="keyword">import</span> random</span><br><span class="line"><span class="keyword">import</span> time</span><br><span class="line"></span><br><span class="line">start = time.time()</span><br><span class="line">als = ALS(rank=<span class="number">10</span>,maxIter=<span class="number">15</span>,regParam=<span class="number">0.01</span>,alpha=<span class="number">1.0</span>,seed=<span class="built_in">int</span>(random.random()*<span class="number">100</span>))</span><br><span class="line">model=als.fit(uaDF)</span><br><span class="line">end = time.time()</span><br><span class="line"><span class="built_in">print</span> (<span class="string">"时间:"</span>+<span class="built_in">str</span>(end-start))</span><br></pre></td></tr></tbody></table></figure><p>输出结果：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">时间:<span class="number">785.1817960739136</span></span><br></pre></td></tr></tbody></table></figure><p>这样我们就构建了一个 ALSModel 模型。</p><p>模型用两个不同的 DataFrame，它们分别表示 “用户 - 特征” 和 “产品 - 特征” 这两个大型矩阵。</p><h3 id="检查推荐结果"><a href="#检查推荐结果" class="headerlink" title="检查推荐结果"></a>检查推荐结果</h3><p>依据构建的模型，选择部分 ID 检查推荐结果。</p><p>看看模型给出的艺术家推荐直观上是否合理，检查一下用户播放过的艺术家，然后看看模型向用户推荐的艺术家。具体来看看用户 2093760 的例子。</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">userID = <span class="number">2093760</span></span><br><span class="line">a=uaDF.rdd.<span class="built_in">filter</span>(<span class="keyword">lambda</span> x:x[<span class="number">0</span>]==userID).collect()</span><br></pre></td></tr></tbody></table></figure><p>查看用户输出结果：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">[</span><br><span class="line">Row(user=<span class="number">2093760</span>, item=<span class="number">1180</span>, rating=<span class="number">1</span>), </span><br><span class="line">Row(user=<span class="number">2093760</span>, item=<span class="number">1255340</span>, rating=<span class="number">3</span>), </span><br><span class="line">Row(user=<span class="number">2093760</span>, item=<span class="number">378</span>, rating=<span class="number">1</span>), </span><br><span class="line">Row(user=<span class="number">2093760</span>, item=<span class="number">813</span>, rating=<span class="number">2</span>), </span><br><span class="line">Row(user=<span class="number">2093760</span>, item=<span class="number">942</span>, rating=<span class="number">7</span>)</span><br><span class="line">] </span><br></pre></td></tr></tbody></table></figure><p>获取艺术家 ID：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">artistid=[]</span><br><span class="line"><span class="keyword">for</span> i <span class="keyword">in</span> a:</span><br><span class="line"> artistid.append(i.item)</span><br></pre></td></tr></tbody></table></figure><p>输出结果：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">[<span class="number">1180</span>, <span class="number">1255340</span>, <span class="number">378</span>, <span class="number">813</span>, <span class="number">942</span>] </span><br></pre></td></tr></tbody></table></figure><p>要提取该用户收听过的艺术家 ID 并打印他们的名字，这意味着先在输入数据中搜索该用户收听过的艺术家的 ID，然后用这些 ID 对艺术家集合进行过滤，这样我们就可以获取并按序打印这些艺术家的名字：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">b=aDF.rdd.<span class="built_in">filter</span>(**<span class="keyword">lambda</span>** x: x[<span class="number">0</span>] **<span class="keyword">in</span>** artistid).collect() </span><br></pre></td></tr></tbody></table></figure><p>输出结果：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">[Row(<span class="built_in">id</span>=<span class="number">1180</span>, name=<span class="string">'David Gray'</span>), </span><br><span class="line"></span><br><span class="line">Row(<span class="built_in">id</span>=<span class="number">378</span>, name=<span class="string">'Blackalicious'</span>), </span><br><span class="line"></span><br><span class="line">Row(<span class="built_in">id</span>=<span class="number">813</span>, name=<span class="string">'Jurassic 5'</span>), </span><br><span class="line"></span><br><span class="line">Row(<span class="built_in">id</span>=<span class="number">1255340</span>, name=<span class="string">'The Saw Doctors'</span>), </span><br><span class="line"></span><br><span class="line">Row(<span class="built_in">id</span>=<span class="number">942</span>, name=<span class="string">'Xzibit'</span>)] </span><br></pre></td></tr></tbody></table></figure><p>用户播放过的艺术家既有大众流行音乐风格的也有嘻哈风格的。</p><p> 使用 Spark2.4.6 自带的 recommendForUserSubset 方法，对所有艺术家评分，并返回向用户 2093760 推荐其中分值最高的前 5 位。</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">d=sc.parallelize([(<span class="number">2093760</span>,<span class="number">1</span>)]).toDF([<span class="string">'user'</span>]) </span><br><span class="line"></span><br><span class="line">t=model.recommendForUserSubset(d,<span class="number">5</span>) </span><br><span class="line"></span><br><span class="line">t.show() </span><br></pre></td></tr></tbody></table></figure><p>输出结果：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">+-------+--------------------+ </span><br><span class="line">| user| recommendations|</span><br><span class="line">+-------+--------------------+</span><br><span class="line">|<span class="number">2093760</span>|[[<span class="number">6674945</span>, <span class="number">4997.0</span>...|</span><br><span class="line">+-------+--------------------+</span><br></pre></td></tr></tbody></table></figure><p>遍历打印一下：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">t.select(<span class="string">"recommendations"</span>).rdd.foreach(**<span class="keyword">lambda</span>** x:**<span class="built_in">print</span>**(x)) </span><br></pre></td></tr></tbody></table></figure><p>输出：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">Row(recommendations=[</span><br><span class="line"> Row(item=<span class="number">6674945</span>, rating=<span class="number">4997.056640625</span>), </span><br><span class="line"> Row(item=<span class="number">1170225</span>, rating=<span class="number">1805.596435546875</span>), </span><br><span class="line"> Row(item=<span class="number">1153293</span>, rating=<span class="number">1753.0908203125</span>), </span><br><span class="line"> Row(item=<span class="number">6730413</span>, rating=<span class="number">1233.61767578125</span>), </span><br><span class="line"> Row(item=<span class="number">183</span>, rating=<span class="number">1169.90234375</span>)</span><br><span class="line">])</span><br></pre></td></tr></tbody></table></figure><p>结果全部是嘻哈风格。能看出，这些推荐都不怎么样。虽然推荐的艺术家都受人欢迎，但好像并没有针对用户的收听习惯进行个性化。</p><h3 id="训练-验证切分"><a href="#训练-验证切分" class="headerlink" title="训练-验证切分"></a>训练 - 验证切分</h3><p>训练 - 验证切分，采用初始参数，重新训练模型。</p><p>为了利用输入数据，需要把它分成训练集和验证集。训练集只用于训练 ALS 模型，验证集用于评估模型。这里将 90% 的数据用于训练，剩余的 10% 用于交叉验证：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">train,test=uaDF.randomSplit([<span class="number">0.9</span>,<span class="number">0.1</span>])</span><br><span class="line">als = ALS(rank=<span class="number">10</span>,maxIter=<span class="number">15</span>,regParam=<span class="number">0.01</span>,alpha=<span class="number">1.0</span>,seed=<span class="built_in">int</span>(random.random()*<span class="number">100</span>),implicitPrefs=<span class="literal">True</span>)</span><br><span class="line">model=als.fit(train)</span><br><span class="line">train.cache()</span><br><span class="line">test.cache()</span><br></pre></td></tr></tbody></table></figure><h3 id="计算AUC"><a href="#计算AUC" class="headerlink" title="计算AUC"></a>计算 AUC</h3><p>接受一个交叉验证集和一个预测函数，交叉验证集代表每个用户对应的 “正面的” 或 “好的” 艺术家。预测函数把每个包含 “用户 - 艺术家” 对的 DataFrame 转换为一个同时包含 “用户 - 艺术家” 和 “预测” 的 DataFrame，“预测” 表示 “用户” 与 “艺术家” 之间关联的强度值，这个值越高，代表推荐的排名越高。</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">allArtistIDs = uaDF.select(<span class="string">"item"</span>).distinct().collect()</span><br><span class="line"></span><br><span class="line"><span class="keyword">import</span> numpy</span><br><span class="line">allArtistID = []</span><br><span class="line"><span class="keyword">for</span> i <span class="keyword">in</span> <span class="built_in">range</span>(<span class="built_in">len</span>(allArtistIDs)):</span><br><span class="line"> allArtistID.append(allArtistIDs[i][<span class="string">"item"</span>])</span><br><span class="line"><span class="keyword">def</span> <span class="title function_">f</span>(<span class="params">a,b</span>):</span><br><span class="line"> posItemIDSet = <span class="built_in">set</span>(<span class="built_in">list</span>(b))</span><br><span class="line"> negative = []</span><br><span class="line"> i = <span class="number">0</span></span><br><span class="line"> <span class="keyword">while</span> (i < <span class="built_in">len</span>(allArtistID)) <span class="keyword">and</span> (<span class="built_in">len</span>(negative) < <span class="built_in">len</span>(posItemIDSet)):</span><br><span class="line"> artistID = allArtistID[numpy.random.randint(<span class="number">1</span>, high=<span class="built_in">len</span>(allArtistID), size=<span class="literal">None</span>, dtype=<span class="string">'l'</span>)]</span><br><span class="line"> <span class="keyword">if</span> artistID <span class="keyword">not</span> <span class="keyword">in</span> posItemIDSet:</span><br><span class="line"> negative.append(artistID)</span><br><span class="line"> i += <span class="number">1</span></span><br><span class="line"> s=<span class="built_in">list</span>()</span><br><span class="line"> <span class="keyword">for</span> i <span class="keyword">in</span> negative:</span><br><span class="line"> s.append((a,i))</span><br><span class="line"> <span class="keyword">return</span> s</span><br><span class="line"></span><br><span class="line"><span class="comment"># 计算AUC</span></span><br><span class="line"><span class="keyword">import</span> pyspark.sql.functions <span class="keyword">as</span> func</span><br><span class="line"><span class="keyword">def</span> <span class="title function_">areaUnderCurve</span>(<span class="params">positiveData,allArtistIDs,predictFunction</span>):</span><br><span class="line"> positivePredictions = predictFunction(positiveData.select(<span class="string">"user"</span>, <span class="string">"item"</span>)).withColumnRenamed(<span class="string">"prediction"</span>, <span class="string">"positivePrediction"</span>)</span><br><span class="line"> negativeDatatmp = positiveData.select(<span class="string">"user"</span>, <span class="string">"item"</span>).rdd.groupByKey().<span class="built_in">map</span>(<span class="keyword">lambda</span> x: f(x[<span class="number">0</span>],x[<span class="number">1</span>])).collect()</span><br><span class="line"> negativeDatalist=[]</span><br><span class="line"> <span class="keyword">for</span> i <span class="keyword">in</span> negativeDatatmp:</span><br><span class="line"> <span class="keyword">for</span> j <span class="keyword">in</span> i:</span><br><span class="line"> negativeDatalist.append(j) </span><br><span class="line"> negativeData=spark.createDataFrame(negativeDatalist,[<span class="string">'user'</span>,<span class="string">'item'</span>])</span><br><span class="line"> negativePredictions = predictFunction(negativeData.select(<span class="string">"user"</span>, <span class="string">"item"</span>)).withColumnRenamed(<span class="string">"prediction"</span>, <span class="string">"negativePrediction"</span>)</span><br><span class="line"> joinedPredictions = positivePredictions.join(negativePredictions, <span class="string">"user"</span>).select(<span class="string">"user"</span>, <span class="string">"positivePrediction"</span>, <span class="string">"negativePrediction"</span>)</span><br><span class="line"> allCounts = joinedPredictions.groupBy(<span class="string">"user"</span>).agg(func.count(func.lit(<span class="number">1</span>)).alias(<span class="string">"total"</span>)).select(<span class="string">"user"</span>, <span class="string">"total"</span>)</span><br><span class="line"> correctCounts = joinedPredictions.<span class="built_in">filter</span>(joinedPredictions[<span class="string">"positivePrediction"</span>] > joinedPredictions[<span class="string">"negativePrediction"</span>]).groupBy(<span class="string">"user"</span>).agg(func.count(<span class="string">"user"</span>).alias(<span class="string">"correct"</span>)).select(<span class="string">"user"</span>, <span class="string">"correct"</span>)</span><br><span class="line"> meanAUCtemp = allCounts.join(correctCounts, <span class="string">"user"</span>, <span class="string">"left_outer"</span>)</span><br><span class="line"> meanAUC = meanAUCtemp.select(<span class="string">"user"</span>, (meanAUCtemp[<span class="string">"correct"</span>] / meanAUCtemp[<span class="string">"total"</span>]).alias(<span class="string">"auc"</span>)).agg(func.mean(<span class="string">"auc"</span>)).first()</span><br><span class="line"> <span class="keyword">try</span>:</span><br><span class="line"> joinedPredictions.unpersist()</span><br><span class="line"> <span class="keyword">except</span>:</span><br><span class="line"> <span class="keyword">pass</span></span><br><span class="line"> <span class="keyword">return</span> meanAUC</span><br><span class="line"> </span><br><span class="line">mostListenedAUC = areaUnderCurve(test, allArtistIDs, model.transform)</span><br><span class="line"><span class="built_in">print</span>(mostListenedAUC)</span><br></pre></td></tr></tbody></table></figure><p>输出结果：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">Row(avg(auc)=<span class="number">0.9098560946043145</span>) </span><br></pre></td></tr></tbody></table></figure><p>有必要把上述方法和一个更简单方法做一个基准比对。举个例子，考虑下面的推荐方法：向每个用户推荐播放最多的艺术家。这个策略一点儿都不个性化，但它很简单，也可能有效。定义这个简单预测函数并评估它的 AUC 得分：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">def</span> <span class="title function_">predictMostListened</span>(<span class="params">data</span>):</span><br><span class="line"> listenCounts = train.groupBy(<span class="string">"item"</span>).agg({<span class="string">"rating"</span>:<span class="string">"sum"</span>}).withColumnRenamed(<span class="string">"sum(rating)"</span>, <span class="string">"prediction"</span>).select(<span class="string">"item"</span>, <span class="string">"prediction"</span>)</span><br><span class="line"> uaDF.join(listenCounts, [<span class="string">"item"</span>], <span class="string">"left_outer"</span>).select(<span class="string">"user"</span>, <span class="string">"item"</span>, <span class="string">"prediction"</span>)</span><br><span class="line"> listenCounts = uaDF.groupBy(<span class="string">"item"</span>).agg({<span class="string">"rating"</span>:<span class="string">"sum"</span>}).withColumnRenamed(<span class="string">"sum(rating)"</span>, <span class="string">"prediction"</span>).select(<span class="string">"item"</span>, <span class="string">"prediction"</span>)</span><br><span class="line"> <span class="keyword">return</span> data.join(listenCounts, [<span class="string">"item"</span>], <span class="string">"left_outer"</span>).select(<span class="string">"user"</span>, <span class="string">"item"</span>, <span class="string">"prediction"</span>)</span><br><span class="line">mostListenedAUC = areaUnderCurve(test, allArtistIDs, predictMostListened)</span><br><span class="line"><span class="built_in">print</span>(mostListenedAUC)</span><br></pre></td></tr></tbody></table></figure><p>输出结果：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">Row(avg(auc)=<span class="number">0.9578054887285846</span>) </span><br></pre></td></tr></tbody></table></figure><p>结果得分大约是 0.96。这意味着，对 AUC 这个指标，非个性化的推荐表现已经不错了。然而，我们想要的是得分更高，也就是更为 “个性化” 的推荐。显然这个模型还有待改进。调整超参数，使推荐结果更合理。</p><h3 id="选择超参数"><a href="#选择超参数" class="headerlink" title="选择超参数"></a>选择超参数</h3><p>Rank 可选（5,30）RegParam 可选（4.0,0.0001）,alpha 可选（1.0,40.0）。合计 8 种参数组合。</p><p>可以把 rank、regParam 和 alpha 看作模型的超参数。（maxIter 更像是对分解过程使用的资源的一种约束。）这些值不会体现在 ALSModel 的内部矩阵中，这些矩阵只是参数，其值由算法选定。超参数则是构建过程本身的参数。</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">def</span> <span class="title function_">TrainALS</span>(<span class="params">rank,regParam,alpha,<span class="built_in">dir</span></span>):</span><br><span class="line"> als = ALS(rank=rank,maxIter=<span class="number">15</span>,regParam=regParam,alpha=alpha,seed=<span class="built_in">int</span>(random.random()*<span class="number">100</span>),implicitPrefs=<span class="literal">True</span>)</span><br><span class="line"> model=als.fit(train)</span><br><span class="line"> model.save(<span class="string">"/model/ALS/Try2/"</span>+<span class="built_in">str</span>(<span class="built_in">dir</span>))</span><br><span class="line"> <span class="keyword">try</span>:</span><br><span class="line"> model.userFactors.unpersist()</span><br><span class="line"> model.itemFactors.unpersist()</span><br><span class="line"> <span class="keyword">except</span>:</span><br><span class="line"> <span class="keyword">pass</span></span><br></pre></td></tr></tbody></table></figure><p> 构建模型</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line"><span class="built_in">dir</span>=<span class="number">0</span></span><br><span class="line"><span class="keyword">for</span> rank <span class="keyword">in</span> [<span class="number">5</span>,<span class="number">30</span>]:</span><br><span class="line"> <span class="keyword">for</span> regParam <span class="keyword">in</span> [<span class="number">4.0</span>,<span class="number">0.0001</span>]:</span><br><span class="line"> <span class="keyword">for</span> alpha <span class="keyword">in</span> [<span class="number">1.0</span>,<span class="number">40.0</span>]:</span><br><span class="line"> <span class="built_in">dir</span>=<span class="built_in">dir</span>+<span class="number">1</span></span><br><span class="line"> TrainALS(rank,regParam,alpha,<span class="built_in">dir</span>)</span><br></pre></td></tr></tbody></table></figure><p>加载模型计算 AUC 得分：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">try</span>:</span><br><span class="line"> model=ALSModel.load(<span class="string">"/model/ALS/Try2/1"</span>)</span><br><span class="line"> mostListenedAUC = areaUnderCurve(test, allArtistIDs, model.transform)</span><br><span class="line"> <span class="built_in">print</span>((mostListenedAUC,(<span class="number">5</span>,<span class="number">4.0</span>,<span class="number">1.0</span>)))</span><br><span class="line"><span class="keyword">except</span>:</span><br><span class="line"> <span class="built_in">print</span>((<span class="string">"ERROR"</span>,(<span class="number">5</span>,<span class="number">4.0</span>,<span class="number">1.0</span>)))</span><br><span class="line"><span class="keyword">try</span>:</span><br><span class="line"> model=ALSModel.load(<span class="string">"/model/ALS/Try2/2"</span>)</span><br><span class="line"> mostListenedAUC = areaUnderCurve(test, allArtistIDs, model.transform)</span><br><span class="line"> <span class="built_in">print</span>((mostListenedAUC,(<span class="number">5</span>,<span class="number">4.0</span>,<span class="number">40.0</span>)))</span><br><span class="line"><span class="keyword">except</span>:</span><br><span class="line"> <span class="built_in">print</span>((<span class="string">"ERROR"</span>,(<span class="number">5</span>,<span class="number">4.0</span>,<span class="number">40.0</span>)))</span><br><span class="line"><span class="keyword">try</span>:</span><br><span class="line"> model=ALSModel.load(<span class="string">"/model/ALS/Try2/3"</span>)</span><br><span class="line"> mostListenedAUC = areaUnderCurve(test, allArtistIDs, model.transform)</span><br><span class="line"> <span class="built_in">print</span>((mostListenedAUC,(<span class="number">5</span>,<span class="number">0.0001</span>,<span class="number">1.0</span>)))</span><br><span class="line"><span class="keyword">except</span>:</span><br><span class="line"> <span class="built_in">print</span>((<span class="string">"ERROR"</span>,(<span class="number">5</span>,<span class="number">0.0001</span>,<span class="number">1.0</span>)))</span><br><span class="line"><span class="keyword">try</span>:</span><br><span class="line"> model=ALSModel.load(<span class="string">"/model/ALS/Try2/4"</span>)</span><br><span class="line"> mostListenedAUC = areaUnderCurve(test, allArtistIDs, model.transform)</span><br><span class="line"> <span class="built_in">print</span>((mostListenedAUC,(<span class="number">5</span>,<span class="number">0.0001</span>,<span class="number">40.0</span>)))</span><br><span class="line"><span class="keyword">except</span>:</span><br><span class="line"> <span class="built_in">print</span>((<span class="string">"ERROR"</span>,(<span class="number">5</span>,<span class="number">0.0001</span>,<span class="number">40.0</span>)))</span><br><span class="line"><span class="keyword">try</span>:</span><br><span class="line"> model=ALSModel.load(<span class="string">"/model/ALS/Try2/5"</span>)</span><br><span class="line"> mostListenedAUC = areaUnderCurve(test, allArtistIDs, model.transform)</span><br><span class="line"> <span class="built_in">print</span>((mostListenedAUC,(<span class="number">30</span>,<span class="number">4.0</span>,<span class="number">1.0</span>)))</span><br><span class="line"><span class="keyword">except</span>:</span><br><span class="line"> <span class="built_in">print</span>((<span class="string">"ERROR"</span>,(<span class="number">30</span>,<span class="number">4.0</span>,<span class="number">1.0</span>)))</span><br><span class="line"><span class="keyword">try</span>:</span><br><span class="line"> model=ALSModel.load(<span class="string">"/model/ALS/Try2/6"</span>)</span><br><span class="line"> mostListenedAUC = areaUnderCurve(test, allArtistIDs, model.transform)</span><br><span class="line"> <span class="built_in">print</span>((mostListenedAUC,(<span class="number">30</span>,<span class="number">4.0</span>,<span class="number">40.0</span>)))</span><br><span class="line"><span class="keyword">except</span>:</span><br><span class="line"> <span class="built_in">print</span>((<span class="string">"ERROR"</span>,(<span class="number">30</span>,<span class="number">4.0</span>,<span class="number">40.0</span>)))</span><br><span class="line"><span class="keyword">try</span>:</span><br><span class="line"> model=ALSModel.load(<span class="string">"/model/ALS/Try2/7"</span>)</span><br><span class="line"> mostListenedAUC = areaUnderCurve(test, allArtistIDs, model.transform)</span><br><span class="line"> <span class="built_in">print</span>((mostListenedAUC,(<span class="number">30</span>,<span class="number">0.0001</span>,<span class="number">1.0</span>)))</span><br><span class="line"><span class="keyword">except</span>:</span><br><span class="line"> <span class="built_in">print</span>((<span class="string">"ERROR"</span>,(<span class="number">30</span>,<span class="number">0.0001</span>,<span class="number">1.0</span>)))</span><br><span class="line"><span class="keyword">try</span>:</span><br><span class="line"> model=ALSModel.load(<span class="string">"/model/ALS/Try2/8"</span>)</span><br><span class="line"> mostListenedAUC = areaUnderCurve(test, allArtistIDs, model.transform)</span><br><span class="line"> <span class="built_in">print</span>((mostListenedAUC,(<span class="number">30</span>,<span class="number">0.0001</span>,<span class="number">40.0</span>)))</span><br><span class="line"><span class="keyword">except</span>:</span><br><span class="line"> <span class="built_in">print</span>((<span class="string">"ERROR"</span>,(<span class="number">30</span>,<span class="number">0.0001</span>,<span class="number">40.0</span>)))</span><br></pre></td></tr></tbody></table></figure><p>输出结果：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">(Row(avg(auc)=<span class="number">0.9122637924972641</span>), (<span class="number">5</span>, <span class="number">4.0</span>, <span class="number">1.0</span>))</span><br><span class="line">(Row(avg(auc)=<span class="number">0.9154223563144587</span>), (<span class="number">5</span>, <span class="number">4.0</span>, <span class="number">40.0</span>))</span><br><span class="line">(Row(avg(auc)=<span class="number">0.9057761909633262</span>), (<span class="number">5</span>, <span class="number">0.0001</span>, <span class="number">1.0</span>))</span><br><span class="line">(Row(avg(auc)=<span class="number">0.9146676967584815</span>), (<span class="number">5</span>, <span class="number">0.0001</span>, <span class="number">40.0</span>))</span><br><span class="line">(Row(avg(auc)=<span class="number">0.9230010545570864</span>), (<span class="number">30</span>, <span class="number">4.0</span>, <span class="number">1.0</span>))</span><br><span class="line">(Row(avg(auc)=<span class="number">0.9275148741094371</span>), (<span class="number">30</span>, <span class="number">4.0</span>, <span class="number">40.0</span>))</span><br><span class="line">(Row(avg(auc)=<span class="number">0.9125799456221803</span>), (<span class="number">30</span>, <span class="number">0.0001</span>, <span class="number">1.0</span>))</span><br><span class="line">(Row(avg(auc)=<span class="number">0.9265221600644649</span>), (<span class="number">30</span>, <span class="number">0.0001</span>, <span class="number">40.0</span>))</span><br></pre></td></tr></tbody></table></figure><p>可以看出 rank = 30，regParam = 4.0，alpha = 40.0 时取得了最优的结果 avg (auc)=0.9275148741094371.</p><p>虽然这些值的绝对差很小，但对于 AUC 值来说，仍然具有一定的意义。有意思的是，参数 alpha 取 40 的时候看起来总是比取 1 表现好。这说明了模型在强调用户听过什么时的表现要比强调用户没听过什么时要好。</p><h3 id="产生推荐"><a href="#产生推荐" class="headerlink" title="产生推荐"></a>产生推荐</h3><p>选取 10 个用户展示推荐结果</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">model=ALSModel.load(<span class="string">"/model/ALS/Try2/6"</span>)</span><br><span class="line">d=sc.parallelize([(<span class="number">2093760</span>,<span class="number">1</span>),(<span class="number">1000002</span>,<span class="number">1</span>),(<span class="number">1006277</span>,<span class="number">1</span>),(<span class="number">1006282</span>,<span class="number">1</span>),(<span class="number">1006283</span>,<span class="number">1</span>),(<span class="number">1006285</span>,<span class="number">1</span>),(<span class="number">1041207</span>,<span class="number">1</span>),(<span class="number">1071489</span>,<span class="number">1</span>),(<span class="number">2025005</span>,<span class="number">1</span>),(<span class="number">2025007</span>,<span class="number">1</span>),]).toDF([<span class="string">'user'</span>])</span><br><span class="line">t=model.recommendForUserSubset(d,<span class="number">5</span>)</span><br><span class="line">t.select(<span class="string">"recommendations"</span>).rdd.foreach(<span class="keyword">lambda</span> x:<span class="built_in">print</span>(x))</span><br></pre></td></tr></tbody></table></figure><p>输出推荐结果：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">Row(recommendations=[Row(item=<span class="number">1010991</span>, rating=<span class="number">1.1815389394760132</span>), Row(item=<span class="number">1245226</span>, rating=<span class="number">1.139704942703247</span>), Row(item=<span class="number">4629</span>, rating=<span class="number">1.1092422008514404</span>), Row(item=<span class="number">1113701</span>, rating=<span class="number">1.1066040992736816</span>), Row(item=<span class="number">1019715</span>, rating=<span class="number">1.10056471824646</span>)])</span><br><span class="line">Row(recommendations=[Row(item=<span class="number">1010921</span>, rating=<span class="number">1.225757122039795</span>), Row(item=<span class="number">1166169</span>, rating=<span class="number">1.1972994804382324</span>), Row(item=<span class="number">1183949</span>, rating=<span class="number">1.184556007385254</span>), Row(item=<span class="number">1082446</span>, rating=<span class="number">1.178223729133606</span>), Row(item=<span class="number">3892</span>, rating=<span class="number">1.1580229997634888</span>)])</span><br><span class="line">Row(recommendations=[Row(item=<span class="number">1028958</span>, rating=<span class="number">1.146733283996582</span>), Row(item=<span class="number">1086774</span>, rating=<span class="number">1.1434733867645264</span>), Row(item=<span class="number">1037761</span>, rating=<span class="number">1.1272671222686768</span>), Row(item=<span class="number">1184419</span>, rating=<span class="number">1.1093372106552124</span>), Row(item=<span class="number">1148170</span>, rating=<span class="number">1.1065270900726318</span>)])</span><br><span class="line">Row(recommendations=[Row(item=<span class="number">1010295</span>, rating=<span class="number">1.2554553747177124</span>), Row(item=<span class="number">3722</span>, rating=<span class="number">1.2187168598175049</span>), Row(item=<span class="number">1024674</span>, rating=<span class="number">1.2044183015823364</span>), Row(item=<span class="number">1009445</span>, rating=<span class="number">1.099776268005371</span>), Row(item=<span class="number">1018746</span>, rating=<span class="number">1.0894378423690796</span>)])</span><br><span class="line">Row(recommendations=[Row(item=<span class="number">1002068</span>, rating=<span class="number">0.9575374126434326</span>), Row(item=<span class="number">1005288</span>, rating=<span class="number">0.9533681273460388</span>), Row(item=<span class="number">2430</span>, rating=<span class="number">0.9476644992828369</span>), Row(item=<span class="number">1002270</span>, rating=<span class="number">0.9428261518478394</span>), Row(item=<span class="number">3909</span>, rating=<span class="number">0.9334102869033813</span>)])</span><br><span class="line">Row(recommendations=[Row(item=<span class="number">1034635</span>, rating=<span class="number">0.606441080570221</span>), Row(item=<span class="number">1000107</span>, rating=<span class="number">0.6010327935218811</span>), Row(item=<span class="number">1000024</span>, rating=<span class="number">0.59807950258255</span>), Row(item=<span class="number">4154</span>, rating=<span class="number">0.5966558456420898</span>), Row(item=<span class="number">1000157</span>, rating=<span class="number">0.5944067239761353</span>)])</span><br><span class="line">Row(recommendations=[Row(item=<span class="number">1034635</span>, rating=<span class="number">0.290438175201416</span>), Row(item=<span class="number">930</span>, rating=<span class="number">0.2857869565486908</span>), Row(item=<span class="number">4267</span>, rating=<span class="number">0.2853849530220032</span>), Row(item=<span class="number">1205</span>, rating=<span class="number">0.2830250561237335</span>), Row(item=<span class="number">1000113</span>, rating=<span class="number">0.2829856276512146</span>)])</span><br><span class="line">Row(recommendations=[Row(item=<span class="number">1002909</span>, rating=<span class="number">1.2324668169021606</span>), Row(item=<span class="number">1653</span>, rating=<span class="number">1.1938585042953491</span>), Row(item=<span class="number">988</span>, rating=<span class="number">1.1880080699920654</span>), Row(item=<span class="number">1003367</span>, rating=<span class="number">1.1807997226715088</span>), Row(item=<span class="number">1009545</span>, rating=<span class="number">1.1761128902435303</span>)])</span><br><span class="line">Row(recommendations=[Row(item=<span class="number">1017017</span>, rating=<span class="number">0.8724791407585144</span>), Row(item=<span class="number">1032349</span>, rating=<span class="number">0.8424116373062134</span>), Row(item=<span class="number">1028433</span>, rating=<span class="number">0.8259942531585693</span>), Row(item=<span class="number">1240603</span>, rating=<span class="number">0.8185747265815735</span>), Row(item=<span class="number">1029602</span>, rating=<span class="number">0.8147093653678894</span>)])</span><br><span class="line">Row(recommendations=[Row(item=<span class="number">1013187</span>, rating=<span class="number">1.2516499757766724</span>), Row(item=<span class="number">1098360</span>, rating=<span class="number">1.2394661903381348</span>), Row(item=<span class="number">1289948</span>, rating=<span class="number">1.2353206872940063</span>), Row(item=<span class="number">1129243</span>, rating=<span class="number">1.2332189083099365</span>), Row(item=<span class="number">1245184</span>, rating=<span class="number">1.1997216939926147</span>)])</span><br></pre></td></tr></tbody></table></figure><p>按照用户顺序将最喜欢的推荐结果输出到文件</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">def</span> <span class="title function_">getp</span>(<span class="params">x</span>):</span><br><span class="line"> f=<span class="built_in">open</span>(<span class="string">"/export/work/result"</span>,<span class="string">"a+"</span>)</span><br><span class="line"> <span class="built_in">print</span>(x,file=f)</span><br><span class="line">u=uaDF.select(<span class="string">"user"</span>).distinct()</span><br><span class="line">t=model.recommendForUserSubset(u,<span class="number">1</span>)</span><br><span class="line">t.rdd.foreach(<span class="keyword">lambda</span> x:getp(x))</span><br></pre></td></tr></tbody></table></figure><p>推荐输出详见 result 文件，以下为部分推荐输出：</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line">Row(user=<span class="number">1000092</span>, recommendations=[Row(item=<span class="number">1002400</span>, rating=<span class="number">1.2386927604675293</span>)]) </span><br><span class="line">Row(user=<span class="number">1000144</span>, recommendations=[Row(item=<span class="number">5221</span>, rating=<span class="number">1.1728830337524414</span>)]) </span><br><span class="line">Row(user=<span class="number">3175</span>, recommendations=[Row(item=<span class="number">1022207</span>, rating=<span class="number">0.282743901014328</span>)]) </span><br><span class="line">Row(user=<span class="number">1000164</span>, recommendations=[Row(item=<span class="number">1034635</span>, rating=<span class="number">0.36578264832496643</span>)]) </span><br><span class="line">Row(user=<span class="number">7340</span>, recommendations=[Row(item=<span class="number">1007903</span>, rating=<span class="number">0.8722475171089172</span>)]) </span><br></pre></td></tr></tbody></table></figure></div></div><div class="footer"></div><div class="article-meta" id="bottom"><div class="new-meta-box"></div></div><div class="prev-next"><a class="prev" href="/notes/Spark/streaming-kafka"><p class="title"><i class="fa-solid fa-chevron-left" aria-hidden="true"></i>SparkStreaming 整合 Kafka</p><p class="content">Spark Streaming 整合 Kafka 需关注两个关键版本：Kafka-0.8 将偏移量（offset）存储于 Zookeeper，高并发场景存在瓶颈；Kafka-0.10 则将 offset 保存至 Kafka 内置特殊 topic，优化读写性能。实时处理需权衡数据一致性策略：At most once（可能丢失）、At least once（可能重复）及 Exactly once（精准一次），后者可通过关闭自动提交并结合 Spark 容错机制与事务实现。</p></a><a class="next" href="/notes/Spark/k-means"><p class="title">基于K均值聚类的网络流量异常检测(pyspark)<i class="fa-solid fa-chevron-right" aria-hidden="true"></i></p><p class="content">基于K均值聚类的网络流量异常检测方法通过PySpark实现，用于识别欺诈、网络攻击及设备故障等新型异常。使用KDD Cup 1999数据集（38个特征），通过迭代计算样本点到中心距离划分聚类，更新中心点至收敛。实验步骤含数据准备、HDFS上传、DataFrame构建及k值选择，评价指标为熵和准确率。</p></a></div><div class="recommended-article"><div 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class="fa-duotone fa-comments"></i> 留言区</p><div id="layoutHelper-comments"></div></article></div><aside id="l_side" itemscope="" itemtype="http://schema.org/WPSideBar"><section class="widget text desktop mobile pjax"><header><a href="/notes/"><i class="fa-duotone fa-book fa-fw" aria-hidden="true"></i> <span class="name">Notes</span></a></header><div class="content"></div></section><section class="widget list group desktop mobile pjax"><header><i class="fa-duotone fa-comet fa-fw" aria-hidden="true"></i> <span class="name">Spark-快速大数据分析技术</span></header><div class="content"><ul class="list entry navigation"><li><a class="flat-box" title="/notes/Spark/" href="/notes/Spark/" active-action="action-notesSpark"><div class="name"> Welcome</div></a></li><li><a class="flat-box" title="/notes/Spark/env" href="/notes/Spark/env" active-action="action-notesSparkenv"><div class="name"> Environment Deployment</div></a></li><li><a class="flat-box" title="/notes/Spark/rdd" href="/notes/Spark/rdd" active-action="action-notesSparkrdd"><div class="name"> RDD</div></a></li><li><a class="flat-box" title="/notes/Spark/streaming" href="/notes/Spark/streaming" active-action="action-notesSparkstreaming"><div class="name"> Streaming</div></a></li><li><a class="flat-box" title="/notes/Spark/streaming-kafka" href="/notes/Spark/streaming-kafka" active-action="action-notesSparkstreaming-kafka"><div class="name"> Kafka</div></a></li><li><a class="flat-box" title="/notes/Spark/als" href="/notes/Spark/als" active-action="action-notesSparkals"><div class="name"> ALS</div></a></li><li><a class="flat-box" title="/notes/Spark/k-means" href="/notes/Spark/k-means" active-action="action-notesSparkk-means"><div class="name"> K-Means</div></a></li></ul></div></section><div class="widget-sticky pjax"><section class="widget toc-wrapper desktop mobile" id="toc-div"><header><i class="fa-duotone fa-list fa-fw" aria-hidden="true"></i> <span class="name">本文目录</span></header><div class="content"><ol class="toc"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E6%95%B0%E6%8D%AE%E9%9B%86"><span class="toc-text">数据集</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#user-artist-data-txt"><span class="toc-text">user_artist_data.txt</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#artist-data-txt"><span class="toc-text">artist_data.txt</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#artist-alias-txt"><span class="toc-text">artist_alias.txt</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E7%AE%97%E6%B3%95"><span class="toc-text">算法</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#%E4%BA%A4%E6%9B%BF%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%98%E6%8E%A8%E8%8D%90%E7%AE%97%E6%B3%95-Alternating-Least-Squares%EF%BC%8CALS"><span class="toc-text">交替最小二乘推荐算法 (Alternating Least Squares，ALS)</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E6%8E%A8%E8%8D%90%E8%B4%A8%E9%87%8F%E8%AF%84%E4%BB%B7%E6%8C%87%E6%A0%87AUC"><span class="toc-text">推荐质量评价指标 AUC</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E5%AE%9E%E9%AA%8C%E8%BF%87%E7%A8%8B"><span class="toc-text">实验过程</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#%E6%95%B0%E6%8D%AE%E9%A2%84%E5%A4%84%E7%90%86"><span class="toc-text">数据预处理</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E8%8E%B7%E5%8F%96%E6%95%B0%E6%8D%AE%E6%96%87%E4%BB%B6%EF%BC%8C%E5%B9%B6%E4%B8%8A%E4%BC%A0%E8%87%B3HDFS"><span class="toc-text">获取数据文件，并上传至 HDFS</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E8%AF%BB%E5%85%A5%E6%95%B0%E6%8D%AE%EF%BC%8C%E8%BD%AC%E6%8D%A2%E6%88%90DataFrame%E5%A4%87%E7%94%A8"><span class="toc-text">读入数据，转换成 DataFrame 备用</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E5%B1%95%E7%A4%BA%E6%95%B0%E6%8D%AE%E6%A0%BC%E5%BC%8F%E5%9F%BA%E6%9C%AC%E7%BB%9F%E8%AE%A1%E4%BF%A1%E6%81%AF"><span class="toc-text">展示数据格式基本统计信息</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E5%9F%BA%E6%9C%AC%E7%BB%9F%E8%AE%A1%E4%BF%A1%E6%81%AF"><span class="toc-text">基本统计信息</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E6%9E%84%E5%BB%BAALS%E6%A8%A1%E5%9E%8B"><span class="toc-text">构建 ALS 模型</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E6%A3%80%E6%9F%A5%E6%8E%A8%E8%8D%90%E7%BB%93%E6%9E%9C"><span class="toc-text">检查推荐结果</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E8%AE%AD%E7%BB%83-%E9%AA%8C%E8%AF%81%E5%88%87%E5%88%86"><span class="toc-text">训练 - 验证切分</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E8%AE%A1%E7%AE%97AUC"><span class="toc-text">计算 AUC</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E9%80%89%E6%8B%A9%E8%B6%85%E5%8F%82%E6%95%B0"><span class="toc-text">选择超参数</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E4%BA%A7%E7%94%9F%E6%8E%A8%E8%8D%90"><span class="toc-text">产生推荐</span></a></li></ol></li></ol></div></section></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div 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