{"id":216,"date":"2023-06-13T23:14:07","date_gmt":"2023-06-13T15:14:07","guid":{"rendered":"http:\/\/106.52.213.145:21080\/?p=216"},"modified":"2023-06-29T00:39:23","modified_gmt":"2023-06-28T16:39:23","slug":"lunwenyuedumatrix-factorization-techniques-for-recommender-systems","status":"publish","type":"post","link":"https:\/\/apifj.com\/index.php\/2023\/06\/13\/lunwenyuedumatrix-factorization-techniques-for-recommender-systems\/","title":{"rendered":"[\u8bba\u6587\u9605\u8bfb]MATRIX FACTORIZATION TECHNIQUES FOR RECOMMENDER SYSTEMS"},"content":{"rendered":"<h1>\u77e9\u9635\u5206\u89e3\u6280\u672f\u7528\u4e8e\u63a8\u8350\u7cfb\u7edf<\/h1>\n<p>Yehuda Koren, Yahoo Research Robert Bell and Chris Volinsky, AT&amp;T Labs\u2014Research<\/p>\n<p>\u6b63\u5982Netflix 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decoding=\"async\" src=\"http:\/\/106.52.213.145:21080\/wp-content\/uploads\/2023\/06\/\u622a\u5716-2023-06-13-\u4e0b\u534811.12.51-909x1024.png\" alt=\"\" \/><\/p>\n<p>\u6f5c\u5728\u56e0\u5b50\u6a21\u578b\u662f\u4e00\u79cd\u66ff\u4ee3\u65b9\u6cd5\uff0c\u5b83\u8bd5\u56fe\u901a\u8fc7\u4ece\u8bc4\u5206\u6a21\u5f0f\u4e2d\u63a8\u65ad\u768420\u5230100\u4e2a\u56e0\u5b50\u6765\u63cf\u8ff0\u7269\u54c1\u548c\u7528\u6237\uff0c\u4ee5\u89e3\u91ca\u8bc4\u5206\u3002\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u8bf4\uff0c\u8fd9\u4e9b\u56e0\u5b50\u6784\u6210\u4e86\u4eba\u5de5\u521b\u9020\u7684\u6b4c\u66f2\u57fa\u56e0\u7684\u8ba1\u7b97\u673a\u5316\u66ff\u4ee3\u54c1\u3002\u5bf9\u4e8e\u7535\u5f71\uff0c\u53d1\u73b0\u7684\u56e0\u5b50\u53ef\u80fd\u8861\u91cf\u660e\u663e\u7684\u7ef4\u5ea6\uff0c\u5982\u559c\u5267\u4e0e\u620f\u5267\u3001\u52a8\u4f5c\u7684\u6570\u91cf\u6216\u9762\u5411\u513f\u7ae5\u7684\u503e\u5411\uff1b\u4e0d\u592a\u660e\u786e\u7684\u7ef4\u5ea6\uff0c\u5982\u89d2\u8272\u53d1\u5c55\u7684\u6df1\u5ea6\u6216\u602a\u7656\uff1b\u6216\u8005\u5b8c\u5168\u65e0\u6cd5\u89e3\u91ca\u7684\u7ef4\u5ea6\u3002\u5bf9\u4e8e\u7528\u6237\u6765\u8bf4\uff0c\u6bcf\u4e2a\u56e0\u5b50\u8861\u91cf\u7684\u662f\u7528\u6237\u5bf9\u5728\u76f8\u5e94\u7535\u5f71\u56e0\u5b50\u4e0a\u5f97\u5206\u9ad8\u7684\u7535\u5f71\u7684\u559c\u597d\u7a0b\u5ea6\u3002<\/p>\n<p>\u56fe2 \u4ee5\u4e24\u4e2a\u7ef4\u5ea6\u7684\u7b80\u5316\u793a\u4f8b\u9610\u8ff0\u4e86\u8fd9\u4e2a\u60f3\u6cd5\u3002\u8003\u8651\u4e24\u4e2a\u5047\u8bbe\u7684\u7ef4\u5ea6\uff0c\u5206\u522b\u4e3a\u5973\u6027\u5bfc\u5411\u4e0e\u7537\u6027\u5bfc\u5411\u4ee5\u53ca\u4e25\u8083\u4e0e\u9003\u907f\u73b0\u5b9e\u3002\u56fe\u4e2d\u663e\u793a\u4e86\u4e00\u4e9b\u77e5\u540d\u7535\u5f71\u548c\u4e00\u4e9b\u865a\u6784\u7528\u6237\u53ef\u80fd\u5728\u8fd9\u4e24\u4e2a\u7ef4\u5ea6\u4e0a\u7684\u4f4d\u7f6e\u3002\u5bf9\u4e8e\u8fd9\u4e2a\u6a21\u578b\uff0c\u7528\u6237\u5bf9\u7535\u5f71\u7684\u9884\u6d4b\u8bc4\u5206\u4e0e\u7535\u5f71\u5728\u56fe\u4e0a\u7684\u4f4d\u7f6e\u548c\u7528\u6237\u5728\u56fe\u4e0a\u7684\u4f4d\u7f6e\u7684\u70b9\u79ef\u76f8\u7b49\uff0c\u76f8\u5bf9\u4e8e\u7535\u5f71\u7684\u5e73\u5747\u8bc4\u5206\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u9884\u8ba1Gus\u4f1a\u559c\u6b22\u300a\u5446\u5b50\u4e0e\u5446\u8d3c\u300b\uff0c\u8ba8\u538c\u300a\u7d2b\u8272\u300b\uff0c\u5e76\u5c06\u300a\u52c7\u6562\u7684\u5fc3\u300b\u8bc4\u4e3a\u5e73\u5747\u6c34\u5e73\u3002\u6ce8\u610f\uff0c\u4e00\u4e9b\u7535\u5f71\uff08\u4f8b\u5982\u300a\u6b27\u6d32\u653b\u7565\u300b\uff09\u548c\u7528\u6237\uff08\u4f8b\u5982Dave\uff09\u5728\u8fd9\u4e24\u4e2a\u7ef4\u5ea6\u4e0a\u88ab\u8ba4\u4e3a\u662f\u76f8\u5bf9\u4e2d\u6027\u7684\u3002<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/106.52.213.145:21080\/wp-content\/uploads\/2023\/06\/\u622a\u5716-2023-06-13-\u4e0b\u534811.13.26-1024x892.png\" alt=\"\" \/><\/p>\n<blockquote>\n<p>\u8ba8\u8bba\u4e86\u63a8\u8350\u7cfb\u7edf\u7684\u7b56\u7565\uff0c\u4e3b\u8981\u6d89\u53ca\u4e24\u79cd\u7b56\u7565\uff1a\u5185\u5bb9\u8fc7\u6ee4\u548c\u534f\u540c\u8fc7\u6ee4\u3002\u5185\u5bb9\u8fc7\u6ee4\u7b56\u7565\u901a\u8fc7\u521b\u5efa\u7528\u6237\u548c\u4ea7\u54c1\u7684\u4e2a\u4eba\u8d44\u6599\u6765\u63cf\u8ff0\u5b83\u4eec\u7684\u7279\u5f81\u3002\u534f\u540c\u8fc7\u6ee4\u662f\u4f9d\u8d56\u4e8e\u7528\u6237\u7684\u8fc7\u53bb\u884c\u4e3a\u3002\u5c3d\u7ba1\u534f\u540c\u8fc7\u6ee4\u53ef\u4ee5\u5904\u7406\u5185\u5bb9\u8fc7\u6ee4\u96be\u4ee5\u6349\u6478\u7684\u6570\u636e\u65b9\u9762\uff0c\u4f46\u5b83\u5b58\u5728\u51b7\u542f\u52a8\u95ee\u9898\uff0c\u5373\u65e0\u6cd5\u5904\u7406\u7cfb\u7edf\u7684\u65b0\u4ea7\u54c1\u548c\u7528\u6237\u3002<\/p>\n<\/blockquote>\n<h2>\u77e9\u9635\u5206\u89e3\u65b9\u6cd5<\/h2>\n<p>\u4e00\u4e9b\u6700\u6210\u529f\u7684\u6f5c\u5728\u56e0\u5b50\u6a21\u578b\u7684\u5b9e\u73b0\u57fa\u4e8e\u77e9\u9635\u5206\u89e3\u3002\u5728\u5176\u57fa\u672c\u5f62\u5f0f\u4e2d\uff0c\u77e9\u9635\u5206\u89e3\u901a\u8fc7\u4ece\u7269\u54c1\u8bc4\u5206\u6a21\u5f0f\u4e2d\u63a8\u65ad\u7684\u56e0\u5b50\u5411\u91cf\u6765\u63cf\u8ff0\u7269\u54c1\u548c\u7528\u6237\u3002\u7269\u54c1\u56e0\u5b50\u548c\u7528\u6237\u56e0\u5b50\u4e4b\u95f4\u7684\u9ad8\u76f8\u4f3c\u5ea6\u53ef\u4ee5\u7528\u4e8e\u8fdb\u884c\u63a8\u8350\u3002\u8fd9\u4e9b\u65b9\u6cd5\u8fd1\u5e74\u6765\u53d8\u5f97\u6d41\u884c\u8d77\u6765\uff0c\u56e0\u4e3a\u5b83\u4eec\u5728\u53ef\u6269\u5c55\u6027\u548c\u9884\u6d4b\u51c6\u786e\u6027\u65b9\u9762\u8868\u73b0\u826f\u597d\u3002\u6b64\u5916\uff0c\u5b83\u4eec\u8fd8\u63d0\u4f9b\u4e86\u5728\u5efa\u6a21\u5404\u79cd\u5b9e\u9645\u60c5\u51b5\u65f6\u7684\u5f88\u5927\u7075\u6d3b\u6027\u3002<\/p>\n<p>\u63a8\u8350\u7cfb\u7edf\u4f9d\u8d56\u4e0d\u540c\u7c7b\u578b\u7684\u8f93\u5165\u6570\u636e\uff0c\u901a\u5e38\u5c06\u8fd9\u4e9b\u6570\u636e\u653e\u7f6e\u5728\u4e00\u4e2a\u77e9\u9635\u4e2d\uff0c\u5176\u4e2d\u4e00\u7ef4\u8868\u793a\u7528\u6237\uff0c\u53e6\u4e00\u7ef4\u8868\u793a\u611f\u5174\u8da3\u7684\u7269\u54c1\u3002\u6700\u65b9\u4fbf\u7684\u6570\u636e\u662f\u9ad8\u8d28\u91cf\u7684\u663e\u5f0f\u53cd\u9988\uff0c\u5305\u62ec\u7528\u6237\u5bf9\u4ea7\u54c1\u5174\u8da3\u7684\u660e\u786e\u8f93\u5165\u3002\u4f8b\u5982\uff0cNetflix\u6536\u96c6\u7535\u5f71\u7684\u661f\u7ea7\u8bc4\u4ef7\uff0cTiVo\u7528\u6237\u901a\u8fc7\u6309\u8d5e\u548c\u8e29\u6309\u94ae\u6765\u8868\u793a\u4ed6\u4eec\u5bf9\u7535\u89c6\u8282\u76ee\u7684\u504f\u597d\u3002\u6211\u4eec\u5c06\u660e\u786e\u7684\u7528\u6237\u53cd\u9988\u79f0\u4e3a\u8bc4\u5206\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u660e\u786e\u7684\u53cd\u9988\u6784\u6210\u4e86\u4e00\u4e2a\u7a00\u758f\u77e9\u9635\uff0c\u56e0\u4e3a\u4efb\u4f55\u5355\u4e2a\u7528\u6237\u53ea\u53ef\u80fd\u5bf9\u4e00\u5c0f\u90e8\u5206\u53ef\u80fd\u7684\u7269\u54c1\u8fdb\u884c\u8bc4\u5206\u3002<\/p>\n<p>\u77e9\u9635\u5206\u89e3\u7684\u4e00\u4e2a\u4f18\u70b9\u662f\u5b83\u5141\u8bb8\u52a0\u5165\u989d\u5916\u7684\u4fe1\u606f\u3002\u5f53\u6ca1\u6709\u663e\u5f0f\u53cd\u9988\u53ef\u7528\u65f6\uff0c\u63a8\u8350\u7cfb\u7edf\u53ef\u4ee5\u4f7f\u7528\u9690\u5f0f\u53cd\u9988\u6765\u63a8\u65ad\u7528\u6237\u7684\u504f\u597d\uff0c\u9690\u5f0f\u53cd\u9988\u901a\u8fc7\u89c2\u5bdf\u7528\u6237\u884c\u4e3a\u95f4\u63a5\u53cd\u6620\u610f\u89c1\uff0c\u5305\u62ec\u8d2d\u4e70\u5386\u53f2\u3001\u6d4f\u89c8\u5386\u53f2\u3001\u641c\u7d22\u6a21\u5f0f\u751a\u81f3\u9f20\u6807\u79fb\u52a8\u3002\u9690\u5f0f\u53cd\u9988\u901a\u5e38\u8868\u793a\u4e8b\u4ef6\u7684\u5b58\u5728\u6216\u4e0d\u5b58\u5728\uff0c\u56e0\u6b64\u901a\u5e38\u7531\u4e00\u4e2a\u586b\u5145\u5bc6\u96c6\u7684\u77e9\u9635\u8868\u793a\u3002<\/p>\n<blockquote>\n<p>\u8be5\u5185\u5bb9\u8ba8\u8bba\u4e86\u6f5c\u5728\u56e0\u5b50\u6a21\u578b\u7684\u4e00\u79cd\u5b9e\u73b0\u65b9\u5f0f\u2014\u2014\u77e9\u9635\u5206\u89e3\uff0c\u5e76\u4ecb\u7ecd\u4e86\u77e9\u9635\u5206\u89e3\u5728\u63a8\u8350\u7cfb\u7edf\u4e2d\u7684\u5e94\u7528\u3002<\/p>\n<\/blockquote>\n<h2>\u57fa\u672c\u7684\u77e9\u9635\u5206\u89e3\u6a21\u578b<\/h2>\n<p>\u77e9\u9635\u5206\u89e3\u6a21\u578b\u5c06\u7528\u6237\u548c\u7269\u54c1\u6620\u5c04\u5230\u4e00\u4e2a\u7ef4\u5ea6\u4e3af\u7684\u5171\u540c\u6f5c\u5728\u56e0\u5b50\u7a7a\u95f4\uff0c\u4f7f\u5f97\u7528\u6237-\u7269\u54c1\u4ea4\u4e92\u53ef\u4ee5\u5728\u8be5\u7a7a\u95f4\u4e2d\u5efa\u6a21\u4e3a\u5185\u79ef\u3002\u56e0\u6b64\uff0c\u6bcf\u4e2a\u7269\u54c1<code class=\"katex-inline\">i<\/code>\u90fd\u4e0e\u4e00\u4e2a\u5411\u91cf<code class=\"katex-inline\">q_i \u2208 R^f<\/code>\u76f8\u5173\u8054\uff0c\u6bcf\u4e2a\u7528\u6237<code class=\"katex-inline\">u<\/code>\u90fd\u4e0e\u4e00\u4e2a\u5411\u91cf<code class=\"katex-inline\">p_u \u2208 R^f<\/code>\u76f8\u5173\u8054\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u7269\u54c1<code class=\"katex-inline\">i<\/code>\uff0c<code class=\"katex-inline\">q_i<\/code>\u7684\u5143\u7d20\u5ea6\u91cf\u4e86\u7269\u54c1\u5728\u8fd9\u4e9b\u56e0\u5b50\u4e0a\u7684\u79ef\u6781\u6216\u6d88\u6781\u7a0b\u5ea6\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u7528\u6237<code class=\"katex-inline\">u<\/code>\uff0c<code class=\"katex-inline\">p_u<\/code>\u7684\u5143\u7d20\u5ea6\u91cf\u4e86\u7528\u6237\u5bf9\u5177\u6709\u76f8\u5e94\u56e0\u5b50\u7684\u9ad8\u5206\u7269\u54c1\u7684\u5174\u8da3\u7a0b\u5ea6\uff0c\u540c\u6837\u53ef\u4ee5\u662f\u79ef\u6781\u6216\u6d88\u6781\u7684\u3002\u5f97\u5230\u7684\u70b9\u79ef<code class=\"katex-inline\">q_i^Tp_u<\/code>\u6355\u6349\u4e86\u7528\u6237<code class=\"katex-inline\">u<\/code>\u548c\u7269\u54c1<code class=\"katex-inline\">i<\/code>\u4e4b\u95f4\u7684\u4ea4\u4e92\u2014\u2014\u7528\u6237\u5bf9\u7269\u54c1\u7279\u5f81\u7684\u6574\u4f53\u5174\u8da3\u3002\u8fd9\u8fd1\u4f3c\u4e8e\u7528\u6237<code class=\"katex-inline\">u<\/code>\u5bf9\u7269\u54c1<code class=\"katex-inline\">i<\/code>\u7684\u8bc4\u5206\uff0c\u7528<code class=\"katex-inline\">r_{ui}<\/code>\u8868\u793a\uff0c\u4ece\u800c\u5f97\u51fa\u4f30\u8ba1\u503c\u3002<\/p>\n<pre><code class=\"language-katex\">\n\\hat{r}_{ui}=q_i^Tp_u\n<\/code><\/pre>\n<p>\u4e3b\u8981\u7684\u6311\u6218\u662f\u8ba1\u7b97\u6bcf\u4e2a\u7269\u54c1\u548c\u7528\u6237\u5230\u56e0\u5b50\u5411\u91cf<code class=\"katex-inline\">q_i<\/code>,<code class=\"katex-inline\">p_u \u2208 R^f<\/code>\u7684\u6620\u5c04\u3002\u5728\u63a8\u8350\u7cfb\u7edf\u5b8c\u6210\u8fd9\u4e2a\u6620\u5c04\u4e4b\u540e\uff0c\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u65b9\u7a0b\u5f0f1\u8f7b\u677e\u5730\u4f30\u8ba1\u7528\u6237\u5bf9\u4efb\u4f55\u7269\u54c1\u7684\u8bc4\u5206\u3002<\/p>\n<p>\u8fd9\u6837\u7684\u6a21\u578b\u4e0e\u5947\u5f02\u503c\u5206\u89e3\uff08Singular Value Decomposition\uff0cSVD\uff09\u5bc6\u5207\u76f8\u5173\uff0cSVD\u662f\u4fe1\u606f\u68c0\u7d22\u4e2d\u7528\u4e8e\u8bc6\u522b\u6f5c\u5728\u8bed\u4e49\u56e0\u5b50\u7684\u4e00\u79cd\u6210\u719f\u6280\u672f\u3002\u5728\u534f\u540c\u8fc7\u6ee4\u9886\u57df\u5e94\u7528SVD\u9700\u8981\u5bf9\u7528\u6237-\u7269\u54c1\u8bc4\u5206\u77e9\u9635\u8fdb\u884c\u56e0\u5b50\u5206\u89e3\u3002\u7531\u4e8e\u7528\u6237-\u7269\u54c1\u8bc4\u5206\u77e9\u9635\u7684\u7a00\u758f\u6027\u5bfc\u81f4\u5927\u91cf\u7f3a\u5931\u503c\uff0c\u8fd9\u5e38\u5e38\u5e26\u6765\u56f0\u96be\u3002\u5f53\u77e9\u9635\u7684\u77e5\u8bc6\u4e0d\u5b8c\u6574\u65f6\uff0c\u4f20\u7edf\u7684SVD\u662f\u672a\u5b9a\u4e49\u7684\u3002\u6b64\u5916\uff0c\u4ec5\u4ec5\u5bf9\u76f8\u5bf9\u8f83\u5c11\u7684\u5df2\u77e5\u6761\u76ee\u8fdb\u884c\u5904\u7406\u5f88\u5bb9\u6613\u5bfc\u81f4\u8fc7\u62df\u5408\u95ee\u9898\u3002<\/p>\n<p>\u65e9\u671f\u7684\u7cfb\u7edf\u4f9d\u9760\u586b\u5145\u7f3a\u5931\u8bc4\u5206\u6765\u4f7f\u8bc4\u5206\u77e9\u9635\u53d8\u5f97\u5bc6\u96c6\u3002\u7136\u800c\uff0c\u586b\u5145\u64cd\u4f5c\u53ef\u80fd\u975e\u5e38\u6602\u8d35\uff0c\u56e0\u4e3a\u5b83\u663e\u8457\u589e\u52a0\u4e86\u6570\u636e\u91cf\u3002\u6b64\u5916\uff0c\u4e0d\u51c6\u786e\u7684\u586b\u5145\u53ef\u80fd\u4f1a\u4e25\u91cd\u626d\u66f2\u6570\u636e\u3002\u56e0\u6b64\uff0c\u8fd1\u671f\u7684\u7814\u7a76\u5efa\u8bae\u76f4\u63a5\u5bf9\u89c2\u6d4b\u5230\u7684\u8bc4\u5206\u8fdb\u884c\u5efa\u6a21\uff0c\u540c\u65f6\u901a\u8fc7\u6b63\u5219\u5316\u6a21\u578b\u907f\u514d\u8fc7\u62df\u5408\u3002\u4e3a\u4e86\u5b66\u4e60\u56e0\u5b50\u5411\u91cf\uff08<code class=\"katex-inline\">p_u<\/code>\u548c<code class=\"katex-inline\">q_i<\/code>\uff09\uff0c\u7cfb\u7edf\u5728\u5df2\u77e5\u8bc4\u5206\u96c6\u4e0a\u6700\u5c0f\u5316\u6b63\u5219\u5316\u7684\u5e73\u65b9\u8bef\u5dee\uff1a<\/p>\n<pre><code class=\"language-katex\">\nmin\\sum_{(u,i)\\in  \u03ba}(r_{ui}-q^T_ip_u)^2+\\lambda(||q_i||^2+||p_u||^2)\n<\/code><\/pre>\n<p>\u8fd9\u91cc\uff0c<code class=\"katex-inline\">\u03ba<\/code>\u662f\u5df2\u77e5<code class=\"katex-inline\">r_{ui}<\/code>\u7684<code class=\"katex-inline\">(u, i)<\/code>\u5bf9\u7684\u96c6\u5408\uff08\u8bad\u7ec3\u96c6\uff09\u3002<\/p>\n<p>\u8be5\u7cfb\u7edf\u901a\u8fc7\u62df\u5408\u5148\u524d\u89c2\u6d4b\u5230\u7684\u8bc4\u5206\u6765\u5b66\u4e60\u6a21\u578b\u3002\u7136\u800c\uff0c\u76ee\u6807\u662f\u4ee5\u4e00\u79cd\u80fd\u591f\u9884\u6d4b\u672a\u6765\u672a\u77e5\u8bc4\u5206\u7684\u65b9\u5f0f\u6765\u63a8\u5e7f\u8fd9\u4e9b\u5148\u524d\u7684\u8bc4\u5206\u3002\u56e0\u6b64\uff0c\u7cfb\u7edf\u5e94\u8be5\u901a\u8fc7\u5bf9\u5b66\u5230\u7684\u53c2\u6570\u8fdb\u884c\u6b63\u5219\u5316\u6765\u907f\u514d\u5bf9\u89c2\u6d4b\u6570\u636e\u8fc7\u62df\u5408\uff0c\u5176\u5927\u5c0f\u53d7\u5230\u60e9\u7f5a\u3002\u5e38\u6570\u03bb\u63a7\u5236\u6b63\u5219\u5316\u7684\u7a0b\u5ea6\uff0c\u901a\u5e38\u901a\u8fc7\u4ea4\u53c9\u9a8c\u8bc1\u786e\u5b9a\u3002Ruslan Salakhutdinov\u548cAndriy Mnih\u7684\u300a\u6982\u7387\u77e9\u9635\u5206\u89e3\u300b\u63d0\u4f9b\u4e86\u6b63\u5219\u5316\u7684\u6982\u7387\u57fa\u7840\u3002<\/p>\n<h2>\u5b66\u4e60\u7b97\u6cd5<\/h2>\n<p>\u6700\u5c0f\u5316\u65b9\u7a0b2\u7684\u4e24\u79cd\u65b9\u6cd5\u662f\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff08stochastic gradient descent\uff09\u548c\u4ea4\u66ff\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff08alternating least squares\uff0cALS\uff09\u3002<\/p>\n<h3>\u968f\u673a\u68af\u5ea6\u4e0b\u964d<\/h3>\n<p>Simon Funk\u5728(<a href=\"http:\/\/sifter.org\/~simon\/journal\/20061211.html\">http:\/\/sifter.org\/~simon\/journal\/20061211.html<\/a>)<br \/>\n\u4e2d\u63a8\u5e7f\u4e86\u5bf9\u65b9\u7a0b2\u7684\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u4f18\u5316\u7b97\u6cd5\uff0c\u5176\u4e2d\u8be5\u7b97\u6cd5\u904d\u5386\u8bad\u7ec3\u96c6\u4e2d\u7684\u6240\u6709\u8bc4\u5206\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u7ed9\u5b9a\u7684\u8bad\u7ec3\u6837\u672c\uff0c\u7cfb\u7edf\u9884\u6d4b<code class=\"katex-inline\">r_{ui}<\/code>\u5e76\u8ba1\u7b97\u76f8\u5173\u7684\u9884\u6d4b\u8bef\u5dee\u3002<\/p>\n<pre><code class=\"language-katex\">\ne_{ui}=r_{ui}-q^T_ip_u\n<\/code><\/pre>\n<p>\u7136\u540e\uff0c\u5b83\u6309\u7167\u68af\u5ea6\u76f8\u53cd\u65b9\u5411\u4e0eg\u6210\u6b63\u6bd4\u7684\u5927\u5c0f\u4fee\u6539\u53c2\u6570\uff0c\u5f97\u5230\uff1a<\/p>\n<pre><code class=\"language-katex\">\n\u00b7\\ \\ q_i\\leftarrow q_i+\\gamma \u00b7(e_{ui}\u00b7p_u-\\lambda q_i)\\\\\n\u00b7\\ \\ p_u\\leftarrow p_u+\\gamma \u00b7(e_{ui}\u00b7q_i-\\lambda p_u)\n<\/code><\/pre>\n<p>\u8fd9\u79cd\u6d41\u884c\u7684\u65b9\u6cd5\uff084-6\uff09\u7ed3\u5408\u4e86\u6613\u4e8e\u5b9e\u73b0\u548c\u76f8\u5bf9\u8f83\u5feb\u7684\u8fd0\u884c\u65f6\u95f4\u3002\u7136\u800c\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u4f7f\u7528\u4ea4\u66ff\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff08ALS\uff09\u4f18\u5316\u662f\u6709\u76ca\u7684\u3002<\/p>\n<h3>\u4ea4\u66ff\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/h3>\n<p>\u56e0\u4e3a<code class=\"katex-inline\">q_i<\/code>\u548c<code class=\"katex-inline\">p_u<\/code> \u90fd\u662f\u672a\u77e5\u6570\uff0c\u6240\u4ee5\u65b9\u7a0b2\u4e0d\u662f\u51f8\u7684\u3002\u7136\u800c\uff0c\u5982\u679c\u6211\u4eec\u56fa\u5b9a\u5176\u4e2d\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u4f18\u5316\u95ee\u9898\u5c31\u53d8\u6210\u4e86\u4e8c\u6b21\u578b\uff0c\u5e76\u53ef\u4ee5\u88ab\u6700\u4f18\u89e3\u6c42\u89e3\u3002\u56e0\u6b64\uff0c\u4ea4\u66ff\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff08ALS\uff09\u7684\u6280\u672f\u5728\u56fa\u5b9a<code class=\"katex-inline\">q_i<\/code> \u548c\u56fa\u5b9a<code class=\"katex-inline\">p_u<\/code> \u4e4b\u95f4\u8fdb\u884c\u4ea4\u66ff\u3002\u5f53\u6240\u6709\u7684<code class=\"katex-inline\">p_u<\/code> \u88ab\u56fa\u5b9a\u65f6\uff0c\u7cfb\u7edf\u901a\u8fc7\u6c42\u89e3\u4e00\u4e2a\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\u91cd\u65b0\u8ba1\u7b97<code class=\"katex-inline\">q_i<\/code> \uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u8fd9\u786e\u4fdd\u6bcf\u4e00\u6b65\u90fd\u4f1a\u51cf\u5c0f\u65b9\u7a0b2\u76f4\u5230\u6536\u655b\u3002<\/p>\n<p>\u867d\u7136\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6bd4ALS\u66f4\u7b80\u5355\u4e14\u66f4\u5feb\uff0c\u4f46\u662f\u5728\u81f3\u5c11\u4e24\u79cd\u60c5\u51b5\u4e0b\uff0cALS\u66f4\u6709\u4f18\u52bf\u3002\u7b2c\u4e00\u79cd\u60c5\u51b5\u662f\u7cfb\u7edf\u53ef\u4ee5\u4f7f\u7528\u5e76\u884c\u5316\u3002\u5728ALS\u4e2d\uff0c\u7cfb\u7edf\u72ec\u7acb\u8ba1\u7b97\u6bcf\u4e2a<code class=\"katex-inline\">q_i<\/code> \uff0c\u800c\u4e0e\u5176\u4ed6\u7269\u54c1\u56e0\u5b50\u65e0\u5173\uff0c\u540c\u65f6\u72ec\u7acb\u8ba1\u7b97\u6bcf\u4e2a<code class=\"katex-inline\">p_u<\/code> \uff0c\u800c\u4e0e\u5176\u4ed6\u7528\u6237\u56e0\u5b50\u65e0\u5173\u3002\u8fd9\u4e3a\u7b97\u6cd5\u63d0\u4f9b\u4e86\u6f5c\u5728\u7684\u5927\u89c4\u6a21\u5e76\u884c\u8ba1\u7b97\u7684\u53ef\u80fd\u6027\u3002\u7b2c\u4e8c\u79cd\u60c5\u51b5\u662f\u5bf9\u4e8e\u4ee5\u9690\u5f0f\u6570\u636e\u4e3a\u4e2d\u5fc3\u7684\u7cfb\u7edf\u3002\u7531\u4e8e\u8bad\u7ec3\u96c6\u4e0d\u80fd\u88ab\u8ba4\u4e3a\u662f\u7a00\u758f\u7684\uff0c\u5bf9\u6bcf\u4e2a\u5355\u72ec\u7684\u8bad\u7ec3\u6837\u672c\u8fdb\u884c\u5faa\u73af\u2014\u2014\u5c31\u50cf\u68af\u5ea6\u4e0b\u964d\u90a3\u6837\u2014\u2014\u662f\u4e0d\u5b9e\u9645\u7684\u3002ALS\u53ef\u4ee5\u6709\u6548\u5730\u5904\u7406\u8fd9\u79cd\u60c5\u51b5\u3002<\/p>\n<h2>\u52a0\u5165\u504f\u5dee<\/h2>\n<p>\u77e9\u9635\u5206\u89e3\u65b9\u6cd5\u5728\u534f\u540c\u8fc7\u6ee4\u4e2d\u7684\u4e00\u4e2a\u597d\u5904\u662f\u5176\u7075\u6d3b\u6027\uff0c\u53ef\u4ee5\u5904\u7406\u5404\u79cd\u6570\u636e\u65b9\u9762\u548c\u5176\u4ed6\u7279\u5b9a\u5e94\u7528\u7684\u8981\u6c42\u3002\u8fd9\u8981\u6c42\u5728\u4fdd\u6301\u76f8\u540c\u7684\u5b66\u4e60\u6846\u67b6\u7684\u540c\u65f6\u5bf9\u65b9\u7a0b1\u8fdb\u884c\u8c03\u6574\u3002\u65b9\u7a0b1\u8bd5\u56fe\u6355\u6349\u7528\u6237\u548c\u7269\u54c1\u4e4b\u95f4\u4ea7\u751f\u4e0d\u540c\u8bc4\u5206\u503c\u7684\u4ea4\u4e92\u4f5c\u7528\u3002\u7136\u800c\uff0c\u89c2\u5bdf\u5230\u7684\u8bc4\u5206\u503c\u7684\u5f88\u5927\u4e00\u90e8\u5206\u53d8\u5316\u662f\u7531\u4e0e\u7528\u6237\u6216\u7269\u54c1\u76f8\u5173\u7684\u6548\u5e94\u5f15\u8d77\u7684\uff0c\u8fd9\u4e9b\u6548\u5e94\u88ab\u79f0\u4e3a\u504f\u5dee\u6216\u622a\u8ddd\uff0c\u4e0e\u4efb\u4f55\u4ea4\u4e92\u4f5c\u7528\u65e0\u5173\u3002\u4f8b\u5982\uff0c\u5178\u578b\u7684\u534f\u540c\u8fc7\u6ee4\u6570\u636e\u8868\u73b0\u51fa\u67d0\u4e9b\u7528\u6237\u7ed9\u51fa\u7684\u8bc4\u5206\u6bd4\u5176\u4ed6\u7528\u6237\u66f4\u9ad8\uff0c\u67d0\u4e9b\u7269\u54c1\u6536\u5230\u7684\u8bc4\u5206\u6bd4\u5176\u4ed6\u7269\u54c1\u66f4\u9ad8\u7684\u7cfb\u7edf\u6027\u503e\u5411\u3002\u6bd5\u7adf\uff0c\u67d0\u4e9b\u4ea7\u54c1\u88ab\u666e\u904d\u8ba4\u4e3a\u6bd4\u5176\u4ed6\u4ea7\u54c1\u66f4\u597d\uff08\u6216\u66f4\u5dee\uff09\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u4ec5\u901a\u8fc7<code class=\"katex-inline\">q_i^T p_u\u7684<\/code>\u4ea4\u4e92\u6765\u89e3\u91ca\u5b8c\u6574\u7684\u8bc4\u5206\u503c\u662f\u4e0d\u660e\u667a\u7684\u3002\u76f8\u53cd\uff0c\u7cfb\u7edf\u8bd5\u56fe\u786e\u5b9a\u4e2a\u522b\u7528\u6237\u6216\u7269\u54c1\u504f\u5dee\u53ef\u4ee5\u89e3\u91ca\u7684\u8fd9\u4e9b\u503c\u7684\u90e8\u5206\uff0c\u5e76\u5c06\u6570\u636e\u4e2d\u4ec5\u6709\u771f\u6b63\u7684\u4ea4\u4e92\u90e8\u5206\u8fdb\u884c\u56e0\u5b50\u5efa\u6a21\u3002\u8bc4\u5206<code class=\"katex-inline\">r_{ui}<\/code> \u4e2d\u6d89\u53ca\u7684\u504f\u5dee\u7684\u4e00\u9636\u8fd1\u4f3c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<pre><code class=\"language-katex\">\nb_{ui}=\\mu+b_i+b_u\n<\/code><\/pre>\n<p>\u8bc4\u5206<code class=\"katex-inline\">r_{ui}<\/code>\u4e2d\u6d89\u53ca\u7684\u504f\u5dee\u88ab\u8868\u793a\u4e3a<code class=\"katex-inline\">b_{ui}<\/code>\uff0c\u5b83\u8003\u8651\u4e86\u7528\u6237\u548c\u7269\u54c1\u7684\u5f71\u54cd\u3002\u6574\u4f53\u5e73\u5747\u8bc4\u5206\u7528<code class=\"katex-inline\">\\mu<\/code>\u8868\u793a\uff1b\u53c2\u6570<code class=\"katex-inline\">b_u<\/code>\u548c<code class=\"katex-inline\">b_i<\/code>\u5206\u522b\u8868\u793a\u7528\u6237<code class=\"katex-inline\">u<\/code>\u548c\u7269\u54c1<code class=\"katex-inline\">i<\/code>\u76f8\u5bf9\u4e8e\u5e73\u5747\u503c\u7684\u89c2\u6d4b\u504f\u5dee\u3002\u4f8b\u5982\uff0c\u5047\u8bbe\u60a8\u60f3\u8981\u5bf9\u7528\u6237Joe\u5bf9\u7535\u5f71\u300a\u6cf0\u5766\u5c3c\u514b\u53f7\u300b\u7684\u8bc4\u5206\u8fdb\u884c\u4e00\u9636\u4f30\u8ba1\u3002\u73b0\u5728\u5047\u8bbe\u6240\u6709\u7535\u5f71\u7684\u5e73\u5747\u8bc4\u5206<code class=\"katex-inline\">\\mu<\/code>\u4e3a3.7\u661f\u7ea7\u3002\u6b64\u5916\uff0c\u6cf0\u5766\u5c3c\u514b\u53f7\u4f18\u4e8e\u5e73\u5747\u6c34\u5e73\uff0c\u6240\u4ee5\u5b83\u7684\u8bc4\u5206\u5f80\u5f80\u6bd4\u5e73\u5747\u503c\u9ad8\u51fa0.5\u661f\u3002\u53e6\u4e00\u65b9\u9762\uff0cJoe\u662f\u4e00\u4e2a\u6311\u5254\u7684\u7528\u6237\uff0c\u4ed6\u7684\u8bc4\u5206\u5f80\u5f80\u6bd4\u5e73\u5747\u503c\u4f4e0.3\u661f\u3002\u56e0\u6b64\uff0cJoe\u5bf9\u300a\u6cf0\u5766\u5c3c\u514b\u53f7\u300b\u7684\u8bc4\u5206\u4f30\u8ba1\u5c06\u662f3.9\u661f\uff083.7 + 0.5 &#8211; 0.3\uff09\u3002\u504f\u5dee\u5c06\u65b9\u7a0b1\u6269\u5c55\u5982\u4e0b\uff1a<\/p>\n<pre><code class=\"language-katex\">\n\\hat{r}_{ui}=\\mu+b_i+b_u+q^T_ip_u\n<\/code><\/pre>\n<p>\u5728\u8fd9\u91cc\uff0c\u89c2\u6d4b\u5230\u7684\u8bc4\u5206\u88ab\u5206\u89e3\u4e3a\u56db\u4e2a\u7ec4\u6210\u90e8\u5206\uff1a\u5168\u5c40\u5e73\u5747\u3001\u7269\u54c1\u504f\u5dee\u3001\u7528\u6237\u504f\u5dee\u548c\u7528\u6237\u7269\u54c1\u4ea4\u4e92\u3002\u8fd9\u6837\u6bcf\u4e2a\u7ec4\u6210\u90e8\u5206\u53ea\u89e3\u91ca\u4e0e\u5176\u76f8\u5173\u7684\u90e8\u5206\u4fe1\u53f7\u3002\u7cfb\u7edf\u901a\u8fc7\u6700\u5c0f\u5316\u5e73\u65b9\u8bef\u5dee\u51fd\u6570\u6765\u8fdb\u884c\u5b66\u4e60\uff1a<\/p>\n<pre><code class=\"language-katex\">\n\\min_{p*,q*,b*}\n\\sum_{(u,i)\\in  \u03ba}(r_{ui}-\\mu-b_u-b_i-q^T_ip_u)^2+\\lambda(||q_i||^2+||p_u||^2+b_u^2+b_i^2)\n<\/code><\/pre>\n<p>\u7531\u4e8e\u504f\u5dee\u5f80\u5f80\u6355\u6349\u5230\u89c2\u6d4b\u4fe1\u53f7\u7684\u5f88\u5927\u90e8\u5206\uff0c\u56e0\u6b64\u51c6\u786e\u5efa\u6a21\u5b83\u4eec\u662f\u81f3\u5173\u91cd\u8981\u7684\u3002\u56e0\u6b64\uff0c\u5176\u4ed6\u7814\u7a76\u63d0\u4f9b\u4e86\u66f4\u590d\u6742\u7684\u504f\u5dee\u6a21\u578b\u3002<\/p>\n<h2>\u989d\u5916\u7684\u8f93\u5165\u6765\u6e90<\/h2>\n<p>\u901a\u5e38\uff0c\u7cfb\u7edf\u5fc5\u987b\u5904\u7406\u51b7\u542f\u52a8\u95ee\u9898\uff0c\u5373\u8bb8\u591a\u7528\u6237\u63d0\u4f9b\u975e\u5e38\u5c11\u7684\u8bc4\u5206\uff0c\u5bfc\u81f4\u5f88\u96be\u5bf9\u4ed6\u4eec\u7684\u559c\u597d\u505a\u51fa\u4e00\u822c\u6027\u7ed3\u8bba\u3002\u7f13\u89e3\u8fd9\u4e2a\u95ee\u9898\u7684\u65b9\u6cd5\u662f\u7ed3\u5408\u5173\u4e8e\u7528\u6237\u7684\u989d\u5916\u4fe1\u606f\u6765\u6e90\u3002\u63a8\u8350\u7cfb\u7edf\u53ef\u4ee5\u4f7f\u7528\u9690\u5f0f\u53cd\u9988\u6765\u4e86\u89e3\u7528\u6237\u7684\u504f\u597d\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5b83\u4eec\u53ef\u4ee5\u6536\u96c6\u884c\u4e3a\u4fe1\u606f\uff0c\u800c\u4e0d\u53d7\u7528\u6237\u63d0\u4f9b\u660e\u786e\u8bc4\u5206\u7684\u610f\u613f\u7684\u9650\u5236\u3002\u4f8b\u5982\uff0c\u96f6\u552e\u5546\u53ef\u4ee5\u5229\u7528\u5ba2\u6237\u7684\u8d2d\u4e70\u8bb0\u5f55\u6216\u6d4f\u89c8\u5386\u53f2\u6765\u4e86\u89e3\u4ed6\u4eec\u7684\u503e\u5411\uff0c\u9664\u4e86\u8fd9\u4e9b\u5ba2\u6237\u53ef\u80fd\u63d0\u4f9b\u7684\u8bc4\u5206\u5916\u3002<\/p>\n<p>\u4e3a\u4e86\u7b80\u5316\u8d77\u89c1\uff0c\u8003\u8651\u4e00\u79cd\u5177\u6709\u5e03\u5c14\u9690\u5f0f\u53cd\u9988\u7684\u60c5\u51b5\u3002<code class=\"katex-inline\">N(u)<\/code>\u8868\u793a\u7528\u6237<code class=\"katex-inline\">u<\/code>\u8868\u8fbe\u4e86\u9690\u5f0f\u504f\u597d\u7684\u7269\u54c1\u96c6\u5408\u3002\u901a\u8fc7\u7528\u6237\u9690\u5f0f\u504f\u597d\u7684\u7269\u54c1\uff0c\u7cfb\u7edf\u5bf9\u7528\u6237\u8fdb\u884c\u4e2a\u4eba\u753b\u50cf\u3002\u5728\u8fd9\u91cc\uff0c\u9700\u8981\u4e00\u4e2a\u65b0\u7684\u7269\u54c1\u56e0\u5b50\u96c6\u5408\uff0c\u5176\u4e2d\u7269\u54c1<code class=\"katex-inline\">i<\/code>\u4e0e<code class=\"katex-inline\">x_i \u2208 R^f<\/code>\u76f8\u5173\u8054\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e\u5728<code class=\"katex-inline\">N(u)<\/code>\u4e2d\u663e\u793a\u4e86\u5bf9\u7269\u54c1\u504f\u597d\u7684\u7528\u6237\uff0c\u5176\u7279\u5f81\u5411\u91cf\u4e3a\uff1a<\/p>\n<pre><code class=\"language-katex\">\n\\sum_{i\\in N(u)}x_i\n<\/code><\/pre>\n<p>\u901a\u5e38\u5bf9\u548c\u8fdb\u884c\u5f52\u4e00\u5316\u662f\u6709\u76ca\u7684\uff0c\u4f8b\u5982\uff0c\u4f7f\u7528\u4ee5\u4e0b\u65b9\u5f0f\u8fdb\u884c\u5904\u7406\uff1a<\/p>\n<pre><code class=\"language-katex\">\n|N(u)|^{-0.5}\\sum_{i\\in N(u)}x_i\n<\/code><\/pre>\n<p>\u53e6\u4e00\u4e2a\u4fe1\u606f\u6765\u6e90\u662f\u5df2\u77e5\u7684\u7528\u6237\u5c5e\u6027\uff0c\u4f8b\u5982\u4eba\u53e3\u7edf\u8ba1\u4fe1\u606f\u3002\u540c\u6837\uff0c\u4e3a\u4e86\u7b80\u5316\u8d77\u89c1\uff0c\u8003\u8651\u5e03\u5c14\u5c5e\u6027\uff0c\u5176\u4e2d\u7528\u6237u\u5bf9\u5e94\u4e8e\u5c5e\u6027\u96c6\u5408<code class=\"katex-inline\">A(u)<\/code>\uff0c\u8be5\u96c6\u5408\u53ef\u4ee5\u63cf\u8ff0\u6027\u522b\u3001\u5e74\u9f84\u7ec4\u3001\u90ae\u653f\u7f16\u7801\u3001\u6536\u5165\u6c34\u5e73\u7b49\u7b49\u3002\u6bcf\u4e2a\u5c5e\u6027\u5bf9\u5e94\u4e00\u4e2a\u4e0d\u540c\u7684\u56e0\u5b50\u5411\u91cf<code class=\"katex-inline\">y_a \u2208 R^f<\/code>\uff0c\u901a\u8fc7\u7528\u6237\u5173\u8054\u7684\u5c5e\u6027\u96c6\u5408\u6765\u63cf\u8ff0\u4e00\u4e2a\u7528\u6237\uff1a<\/p>\n<pre><code class=\"language-katex\">\n\\sum_{a\\in A(u)}y_a\n<\/code><\/pre>\n<p>\u77e9\u9635\u5206\u89e3\u6a21\u578b\u5e94\u8be5\u6574\u5408\u6240\u6709\u7684\u4fe1\u53f7\u6765\u6e90\uff0c\u5e76\u63d0\u5347\u7528\u6237\u7684\u8868\u793a\u80fd\u529b\uff1a<\/p>\n<pre><code class=\"language-katex\">\n\\hat{r}_{ui}=\\mu+b_i+b_u+q^T_i[p_u+|N(u)|^{-0.5}\\sum_{i\\in N(u)}x_i+\\sum_{a\\in A(u)}y_a]\n<\/code><\/pre>\n<p>\u5c3d\u7ba1\u524d\u9762\u7684\u4f8b\u5b50\u6d89\u53ca\u589e\u5f3a\u7528\u6237\u8868\u793a\uff08\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6570\u636e\u7f3a\u4e4f\u66f4\u4e3a\u666e\u904d\uff09\uff0c\u4f46\u5f53\u9700\u8981\u65f6\uff0c\u7269\u54c1\u4e5f\u53ef\u4ee5\u5f97\u5230\u7c7b\u4f3c\u7684\u5904\u7406\u3002<\/p>\n<h2>\u65f6\u95f4\u52a8\u6001<\/h2>\n<p>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6240\u4ecb\u7ecd\u7684\u6a21\u578b\u90fd\u662f\u9759\u6001\u7684\u3002\u5b9e\u9645\u4e0a\uff0c\u4ea7\u54c1\u7684\u8ba4\u77e5\u548c\u53d7\u6b22\u8fce\u7a0b\u5ea6\u4e0d\u65ad\u53d8\u5316\uff0c\u968f\u7740\u65b0\u7684\u9009\u62e9\u7684\u51fa\u73b0\u3002\u540c\u6837\uff0c\u987e\u5ba2\u7684\u503e\u5411\u4e5f\u5728\u6f14\u53d8\uff0c\u5bfc\u81f4\u4ed6\u4eec\u91cd\u65b0\u5b9a\u4e49\u81ea\u5df1\u7684\u53e3\u5473\u3002\u56e0\u6b64\uff0c\u7cfb\u7edf\u5e94\u8be5\u8003\u8651\u53cd\u6620\u7528\u6237\u4e0e\u7269\u54c1\u4ea4\u4e92\u7684\u52a8\u6001\u3001\u968f\u65f6\u95f4\u6f02\u79fb\u7684\u65f6\u95f4\u6548\u5e94\u3002<\/p>\n<p>\u77e9\u9635\u5206\u89e3\u65b9\u6cd5\u975e\u5e38\u9002\u5408\u5efa\u6a21\u65f6\u95f4\u6548\u5e94\uff0c\u53ef\u4ee5\u663e\u8457\u63d0\u9ad8\u51c6\u786e\u6027\u3002\u5c06\u8bc4\u5206\u5206\u89e3\u4e3a\u4e0d\u540c\u7684\u9879\u4f7f\u7cfb\u7edf\u80fd\u591f\u5355\u72ec\u5904\u7406\u4e0d\u540c\u7684\u65f6\u95f4\u65b9\u9762\u3002\u5177\u4f53\u800c\u8a00\uff0c\u4ee5\u4e0b\u9879\u968f\u65f6\u95f4\u53d8\u5316\uff1a\u7269\u54c1\u504f\u5dee<code class=\"katex-inline\">b_i(t)<\/code>\u3001\u7528\u6237\u504f\u5dee<code class=\"katex-inline\">b_u(t)<\/code>\u548c\u7528\u6237\u504f\u597d<code class=\"katex-inline\">p_u(t)<\/code>\u3002<\/p>\n<p>\u7b2c\u4e00\u4e2a\u65f6\u95f4\u6548\u5e94\u6d89\u53ca\u5230\u7269\u54c1\u7684\u53d7\u6b22\u8fce\u7a0b\u5ea6\u53ef\u80fd\u968f\u65f6\u95f4\u53d8\u5316\u3002\u4f8b\u5982\uff0c\u7535\u5f71\u7684\u53d7\u6b22\u8fce\u7a0b\u5ea6\u53ef\u80fd\u56e0\u4e3a\u5916\u90e8\u4e8b\u4ef6\uff08\u6bd4\u5982\u6f14\u5458\u51fa\u73b0\u5728\u65b0\u7535\u5f71\u4e2d\uff09\u800c\u4e0a\u4e0b\u6ce2\u52a8\u3002\u56e0\u6b64\uff0c\u8fd9\u4e9b\u6a21\u578b\u5c06\u7269\u54c1\u504f\u5dee<code class=\"katex-inline\">b_i<\/code>\u89c6\u4e3a\u65f6\u95f4\u7684\u51fd\u6570\u3002\u7b2c\u4e8c\u4e2a\u65f6\u95f4\u6548\u5e94\u5141\u8bb8\u7528\u6237\u968f\u65f6\u95f4\u6539\u53d8\u5176\u57fa\u51c6\u8bc4\u5206\u3002\u4f8b\u5982\uff0c\u4e00\u4e2a\u503e\u5411\u4e8e\u7ed9\u4e00\u90e8\u666e\u901a\u7535\u5f71\u8bc4\u5206\u201c4\u661f\u201d\u7684\u7528\u6237\u73b0\u5728\u53ef\u80fd\u7ed9\u8fd9\u6837\u7684\u7535\u5f71\u8bc4\u5206\u201c3\u661f\u201d\u3002\u8fd9\u53ef\u80fd\u53cd\u6620\u4e86\u591a\u79cd\u56e0\u7d20\uff0c\u5305\u62ec\u7528\u6237\u8bc4\u5206\u6807\u51c6\u7684\u81ea\u7136\u6f02\u79fb\u3001\u7528\u6237\u76f8\u5bf9\u4e8e\u5176\u4ed6\u8fd1\u671f\u8bc4\u5206\u7684\u8bc4\u5206\u8d4b\u503c\uff0c\u4ee5\u53ca\u8bc4\u5206\u8005\u5728\u4e00\u4e2a\u5bb6\u5ead\u4e2d\u7684\u8eab\u4efd\u968f\u65f6\u95f4\u53d8\u5316\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u4e9b\u6a21\u578b\u4e2d\uff0c\u53c2\u6570<code class=\"katex-inline\">b_u<\/code>\u662f\u65f6\u95f4\u7684\u51fd\u6570\u3002<\/p>\n<p>\u65f6\u95f4\u52a8\u6001\u4e0d\u4ec5\u4ec5\u5f71\u54cd\u7269\u54c1\u7684\u53d7\u6b22\u8fce\u7a0b\u5ea6\u548c\u7528\u6237\u7684\u57fa\u51c6\u8bc4\u5206\uff0c\u8fd8\u5f71\u54cd\u7528\u6237\u7684\u504f\u597d\u4ee5\u53ca\u7528\u6237\u4e0e\u7269\u54c1\u4e4b\u95f4\u7684\u4e92\u52a8\u3002\u7528\u6237\u7684\u504f\u597d\u968f\u65f6\u95f4\u53d8\u5316\u3002\u4f8b\u5982\uff0c\u4e00\u4e2a\u5fc3\u7406\u60ca\u609a\u7247\u7684\u7c89\u4e1d\u53ef\u80fd\u4e00\u5e74\u540e\u6210\u4e3a\u72af\u7f6a\u5267\u7684\u7c89\u4e1d\u3002\u540c\u6837\uff0c\u4eba\u4eec\u5bf9\u67d0\u4e9b\u6f14\u5458\u548c\u5bfc\u6f14\u7684\u770b\u6cd5\u4e5f\u4f1a\u6539\u53d8\u3002\u6a21\u578b\u901a\u8fc7\u5c06\u7528\u6237\u56e0\u5b50\uff08\u5411\u91cf<code class=\"katex-inline\">p_u<\/code>\uff09\u4f5c\u4e3a\u65f6\u95f4\u7684\u51fd\u6570\u6765\u8003\u8651\u8fd9\u79cd\u6548\u5e94\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6a21\u578b\u6307\u5b9a\u9759\u6001\u7684\u7269\u54c1\u7279\u5f81<code class=\"katex-inline\">q_i<\/code>\uff0c\u56e0\u4e3a\u4e0e\u4eba\u4e0d\u540c\uff0c\u7269\u54c1\u7684\u6027\u8d28\u662f\u9759\u6001\u7684\u3002<\/p>\n<p>\u7cbe\u786e\u7684\u65f6\u95f4\u53d8\u5316\u53c2\u6570\u5316\u4f1a\u5bfc\u81f4\u7528\u65f6\u95f4\u52a8\u6001\u9884\u6d4b\u89c4\u5219\u66ff\u6362\u65b9\u7a0b4\uff0c\u7528\u4e8e\u5728\u65f6\u95f4t\u65f6\u7684\u8bc4\u5206\u9884\u6d4b\uff1a<\/p>\n<pre><code class=\"language-katex\">\n\\hat{r}_{ui}(t)=u+b_i(t)+b_u(t)+p_u(t)\n<\/code><\/pre>\n<h2>\u5177\u6709\u4e0d\u540c\u7f6e\u4fe1\u6c34\u5e73\u7684\u8f93\u5165<\/h2>\n<p>\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u4e0d\u662f\u6240\u6709\u89c2\u5bdf\u5230\u7684\u8bc4\u5206\u90fd\u5e94\u88ab\u8d4b\u4e88\u76f8\u540c\u7684\u6743\u91cd\u6216\u7f6e\u4fe1\u5ea6\u3002\u4f8b\u5982\uff0c\u5927\u89c4\u6a21\u7684\u5e7f\u544a\u53ef\u80fd\u4f1a\u5f71\u54cd\u67d0\u4e9b\u7269\u54c1\u7684\u8bc4\u5206\uff0c\u8fd9\u4e9b\u8bc4\u5206\u53ef\u80fd\u4e0d\u51c6\u786e\u5730\u53cd\u6620\u4e86\u957f\u671f\u7279\u5f81\u3002\u540c\u6837\uff0c\u7cfb\u7edf\u53ef\u80fd\u9762\u4e34\u654c\u5bf9\u7528\u6237\u7684\u5e72\u6270\uff0c\u4ed6\u4eec\u8bd5\u56fe\u64cd\u7eb5\u67d0\u4e9b\u7269\u54c1\u7684\u8bc4\u5206\u3002<\/p>\n<p>\u53e6\u4e00\u4e2a\u4f8b\u5b50\u662f\u5efa\u7acb\u5728\u9690\u5f0f\u53cd\u9988\u4e0a\u7684\u7cfb\u7edf\u3002\u5728\u8fd9\u79cd\u7cfb\u7edf\u4e2d\uff0c\u901a\u8fc7\u89e3\u8bfb\u7528\u6237\u7684\u6301\u7eed\u884c\u4e3a\uff0c\u5f88\u96be\u7cbe\u786e\u91cf\u5316\u7528\u6237\u7684\u504f\u597d\u6c34\u5e73\u3002\u56e0\u6b64\uff0c\u7cfb\u7edf\u4f7f\u7528\u66f4\u7c97\u7cd9\u7684\u4e8c\u5143\u8868\u793a\uff0c\u5373\u8981\u4e48\u8868\u793a\u201c\u53ef\u80fd\u559c\u6b22\u8be5\u4ea7\u54c1\u201d\uff0c\u8981\u4e48\u8868\u793a\u201c\u53ef\u80fd\u5bf9\u8be5\u4ea7\u54c1\u4e0d\u611f\u5174\u8da3\u201d\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9644\u52a0\u7f6e\u4fe1\u5ea6\u5206\u6570\u5230\u4f30\u8ba1\u7684\u504f\u597d\u662f\u6709\u4ef7\u503c\u7684\u3002\u7f6e\u4fe1\u5ea6\u53ef\u4ee5\u6e90\u81ea\u53ef\u7528\u7684\u6570\u5b57\u503c\uff0c\u7528\u4e8e\u63cf\u8ff0\u884c\u4e3a\u7684\u9891\u7387\uff0c\u4f8b\u5982\u7528\u6237\u89c2\u770b\u67d0\u4e2a\u8282\u76ee\u7684\u65f6\u95f4\u6216\u7528\u6237\u8d2d\u4e70\u67d0\u4e2a\u7269\u54c1\u7684\u9891\u7387\u3002\u8fd9\u4e9b\u6570\u5b57\u503c\u8868\u793a\u4e86\u6bcf\u4e2a\u89c2\u5bdf\u7684\u7f6e\u4fe1\u5ea6\u3002\u4e0e\u7528\u6237\u504f\u597d\u65e0\u5173\u7684\u5404\u79cd\u56e0\u7d20\u53ef\u80fd\u5f15\u8d77\u4e00\u6b21\u6027\u4e8b\u4ef6\uff1b\u7136\u800c\uff0c\u91cd\u590d\u4e8b\u4ef6\u66f4\u6709\u53ef\u80fd\u53cd\u6620\u7528\u6237\u610f\u89c1\u3002<\/p>\n<p>\u9635\u5206\u89e3\u6a21\u578b\u53ef\u4ee5\u8f7b\u677e\u63a5\u53d7\u4e0d\u540c\u7684\u7f6e\u4fe1\u6c34\u5e73\uff0c\u4ece\u800c\u4f7f\u5176\u5bf9\u4e0d\u592a\u6709\u610f\u4e49\u7684\u89c2\u5bdf\u7ed3\u679c\u7ed9\u4e88\u8f83\u4f4e\u7684\u6743\u91cd\u3002\u5982\u679c\u89c2\u5bdf\u5230<code class=\"katex-inline\">r_{ui}<\/code> \u7684\u7f6e\u4fe1\u5ea6\u8868\u793a\u4e3a<code class=\"katex-inline\">c_{ui}<\/code> \uff0c\u90a3\u4e48\u6a21\u578b\u4f1a\u4fee\u6539\u6210\u672c\u51fd\u6570\uff08\u65b9\u7a0b5\uff09\uff0c\u4ee5\u8003\u8651\u7f6e\u4fe1\u5ea6\u7684\u5f71\u54cd\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<pre><code class=\"language-katex\">\n\\min_{p*,q*,b*}\n\\sum_{(u,i)\\in  \u03ba}c_{ui}(r_{ui}-\\mu-b_u-b_i-q^T_ip_u)^2+\\lambda(||q_i||^2+||p_u||^2+b_u^2+b_i^2)\n<\/code><\/pre>\n<p>\u6709\u5173\u6d89\u53ca\u6b64\u7c7b\u65b9\u6848\u7684\u5b9e\u9645\u5e94\u7528\u7684\u4fe1\u606f\uff0c\u8bf7\u53c2\u9605\u300a\u7528\u4e8e\u9690\u5f0f\u53cd\u9988\u6570\u636e\u96c6\u7684\u534f\u540c\u8fc7\u6ee4\u300b\u3002<\/p>\n<h2>Netflix Prize\u7ade\u8d5b<\/h2>\n<p>\u57282006\u5e74\uff0c\u5728\u7ebfDVD\u79df\u8d41\u516c\u53f8Netflix\u5ba3\u5e03\u4e86\u4e00\u9879\u7ade\u8d5b\uff0c\u65e8\u5728\u6539\u8fdb\u5176\u63a8\u8350\u7cfb\u7edf\u3002\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e00\u76ee\u6807\uff0c\u8be5\u516c\u53f8\u53d1\u5e03\u4e86\u4e00\u4e2a\u8bad\u7ec3\u96c6\uff0c\u5176\u4e2d\u5305\u542b\u8d85\u8fc71\u4ebf\u6761\u8bc4\u5206\u6570\u636e\uff0c\u6db5\u76d6\u4e86\u7ea650\u4e07\u4e2a\u533f\u540d\u7528\u6237\u5bf9\u8d85\u8fc717,000\u90e8\u7535\u5f71\u7684\u8bc4\u5206\uff0c\u6bcf\u90e8\u7535\u5f71\u7684\u8bc4\u5206\u8303\u56f4\u662f1\u52305\u9897\u661f\u3002\u53c2\u4e0e\u7684\u56e2\u961f\u9700\u8981\u63d0\u4ea4\u5bf9\u5927\u7ea63\u767e\u4e07\u6761\u8bc4\u5206\u7684\u6d4b\u8bd5\u96c6\u7684\u9884\u6d4b\u8bc4\u5206\uff0cNetflix\u6839\u636e\u4fdd\u7559\u7684\u771f\u5b9e\u8bc4\u5206\u8ba1\u7b97\u5747\u65b9\u6839\u8bef\u5dee\uff08RMSE\uff09\u3002\u5982\u679c\u6709\u56e2\u961f\u80fd\u591f\u5c06Netflix\u7b97\u6cd5\u7684RMSE\u6027\u80fd\u63d0\u9ad810%\u6216\u66f4\u591a\uff0c\u4ed6\u4eec\u5c06\u8d62\u5f97100\u4e07\u7f8e\u5143\u7684\u5956\u91d1\u3002\u5982\u679c\u6ca1\u6709\u56e2\u961f\u8fbe\u523010%\u7684\u76ee\u6807\uff0cNetflix\u5c06\u5728\u6bcf\u5e74\u7684\u7ade\u8d5b\u7ed3\u675f\u540e\u5411\u6392\u540d\u7b2c\u4e00\u7684\u56e2\u961f\u9881\u53d15\u4e07\u7f8e\u5143\u7684\u8fdb\u5c55\u5956\u3002<\/p>\n<p>\u8be5\u7ade\u8d5b\u5728\u534f\u540c\u8fc7\u6ee4\u9886\u57df\u5f15\u8d77\u4e86\u8f70\u52a8\u3002\u5728\u6b64\u4e4b\u524d\uff0c\u516c\u5f00\u53ef\u7528\u7684\u534f\u540c\u8fc7\u6ee4\u7814\u7a76\u6570\u636e\u89c4\u6a21\u8f83\u5c0f\u3002\u8fd9\u4efd\u6570\u636e\u7684\u53d1\u5e03\u548c\u7ade\u8d5b\u7684\u5438\u5f15\u529b\u6fc0\u53d1\u4e86\u5927\u91cf\u7684\u70ed\u60c5\u548c\u6d3b\u52a8\u3002\u6839\u636e\u7ade\u8d5b\u7f51\u7ad9\uff08www.netflixprize.com\uff09\u7684\u6570\u636e\u663e\u793a\uff0c\u6765\u81ea182\u4e2a\u4e0d\u540c\u56fd\u5bb6\u768448,000\u591a\u4e2a\u56e2\u961f\u5df2\u7ecf\u4e0b\u8f7d\u4e86\u8fd9\u4e9b\u6570\u636e\u3002<\/p>\n<p>\u6211\u4eec\u56e2\u961f\u7684\u53c2\u8d5b\u4f5c\u54c1\u6700\u521d\u88ab\u79f0\u4e3aBellKor\uff0c\u57282007\u5e74\u590f\u5b63\u593a\u5f97\u4e86\u7ade\u8d5b\u7684\u51a0\u519b\uff0c\u5e76\u4ee5\u5f53\u65f6\u6700\u597d\u7684\u6210\u7ee9\u8d62\u5f97\u4e862007\u5e74\u7684\u8fdb\u5c55\u5956\uff1a\u6bd4Netflix\u9ad8\u51fa8.43\uff05\u3002\u540e\u6765\uff0c\u6211\u4eec\u4e0eBig Chaos\u56e2\u961f\u5408\u4f5c\uff0c\u4ee59.46\uff05\u7684\u6210\u7ee9\u8d62\u5f97\u4e862008\u5e74\u7684\u8fdb\u5c55\u5956\u3002\u622a\u81f3\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u4ecd\u7136\u6392\u540d\u7b2c\u4e00\uff0c\u9010\u6e10\u63a5\u8fd110\uff05\u7684\u91cc\u7a0b\u7891\u3002<\/p>\n<p>\u6211\u4eec\u83b7\u80dc\u7684\u4f5c\u54c1\u5305\u62ec100\u591a\u4e2a\u4e0d\u540c\u7684\u9884\u6d4b\u5668\u96c6\u5408\uff0c\u5176\u4e2d\u5927\u591a\u6570\u662f\u4f7f\u7528\u672c\u6587\u63cf\u8ff0\u7684\u65b9\u6cd5\u7684\u5404\u79cd\u53d8\u4f53\u7684\u56e0\u5b50\u5206\u89e3\u6a21\u578b\u3002\u6211\u4eec\u4e0e\u5176\u4ed6\u9876\u7ea7\u56e2\u961f\u7684\u8ba8\u8bba\u4ee5\u53ca\u5728\u516c\u5f00\u7ade\u8d5b\u8bba\u575b\u4e0a\u7684\u5e16\u5b50\u8868\u660e\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u662f\u6700\u53d7\u6b22\u8fce\u548c\u6210\u529f\u7684\u7528\u4e8e\u9884\u6d4b\u8bc4\u5206\u7684\u65b9\u6cd5\u3002<br \/>\n<img decoding=\"async\" src=\"http:\/\/106.52.213.145:21080\/wp-content\/uploads\/2023\/06\/\u622a\u5716-2023-06-29-\u4e0a\u534812.37.23-1024x915.png\" alt=\"\" \/><\/p>\n<p>\u901a\u8fc7\u5bf9Netflix\u7528\u6237-\u7535\u5f71\u77e9\u9635\u8fdb\u884c\u56e0\u5b50\u5206\u89e3\uff0c\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\u9884\u6d4b\u7535\u5f71\u504f\u597d\u7684\u6700\u5177\u63cf\u8ff0\u6027\u7684\u7ef4\u5ea6\u3002\u6211\u4eec\u53ef\u4ee5\u4ece\u77e9\u9635\u5206\u89e3\u4e2d\u8bc6\u522b\u51fa\u524d\u51e0\u4e2a\u6700\u91cd\u8981\u7684\u7ef4\u5ea6\uff0c\u5e76\u63a2\u7d22\u7535\u5f71\u5728\u8fd9\u4e2a\u65b0\u7a7a\u95f4\u4e2d\u7684\u4f4d\u7f6e\u3002\u56fe3\u5c55\u793a\u4e86Netflix\u6570\u636e\u77e9\u9635\u5206\u89e3\u7684\u524d\u4e24\u4e2a\u56e0\u5b50\u3002\u7535\u5f71\u6839\u636e\u5b83\u4eec\u7684\u56e0\u5b50\u5411\u91cf\u8fdb\u884c\u6392\u5217\u3002\u719f\u6089\u8fd9\u4e9b\u7535\u5f71\u7684\u4eba\u53ef\u4ee5\u5728\u6f5c\u5728\u56e0\u5b50\u4e2d\u770b\u5230\u660e\u663e\u7684\u542b\u4e49\u3002\u7b2c\u4e00\u4e2a\u56e0\u5b50\u5411\u91cf\uff08x\u8f74\uff09\u7684\u4e00\u4fa7\u662f\u9762\u5411\u7537\u6027\u6216\u9752\u5c11\u5e74\u89c2\u4f17\u7684\u4f4e\u4fd7\u559c\u5267\u548c\u6050\u6016\u7535\u5f71\uff08Half Baked, Freddy vs. Jason\uff09\uff0c\u800c\u53e6\u4e00\u4fa7\u5219\u662f\u5e26\u6709\u4e25\u8083\u542b\u4e49\u548c\u5f3a\u70c8\u5973\u6027\u4e3b\u89d2\u7684\u620f\u5267\u6216\u559c\u5267\uff08Sophie\u2019s Choice, Moonstruck\uff09\u3002\u7b2c\u4e8c\u4e2a\u56e0\u5b50\u5316\u8f74\uff08y\u8f74\uff09\u7684\u9876\u90e8\u662f\u72ec\u7acb\u7684\u3001\u5907\u53d7\u597d\u8bc4\u7684\u3001\u53e4\u602a\u7684\u7535\u5f71\uff08Punch-Drunk Love, I Heart Huckabees\uff09\uff0c\u800c\u5e95\u90e8\u662f\u4e3b\u6d41\u516c\u5f0f\u5316\u7684\u7535\u5f71\uff08Armageddon, Runaway Bride\uff09\u3002\u5728\u8fd9\u4e9b\u8fb9\u754c\u4e4b\u95f4\u5b58\u5728\u6709\u8da3\u7684\u4ea4\u53c9\u70b9\uff1a\u5728\u5de6\u4e0a\u89d2\uff0c\u72ec\u7acb\u7535\u5f71\u4e0e\u4f4e\u4fd7\u7535\u5f71\u76f8\u9047\uff0c\u6709Kill Bill\u548cNatural Born Killers\uff0c\u8fd9\u4e24\u90e8\u827a\u672f\u7535\u5f71\u6d89\u53ca\u66b4\u529b\u4e3b\u9898\u3002\u5728\u53f3\u4e0b\u65b9\uff0c\u4e25\u8083\u7684\u5973\u6027\u4e3b\u5bfc\u7535\u5f71\u4e0e\u4e3b\u6d41\u53d7\u4f17\u559c\u7231\u7684\u7535\u5f71\u76f8\u9047\uff0c\u6709The Sound of Music\u3002\u800c\u5728\u4e2d\u95f4\uff0c\u5438\u5f15\u6240\u6709\u7c7b\u578b\u89c2\u4f17\u7684\u662fThe Wizard of Oz\u3002<\/p>\n<p>\u5728\u8fd9\u4e2a\u56fe\u4e2d\uff0c\u4e00\u4e9b\u76f8\u90bb\u7684\u7535\u5f71\u901a\u5e38\u4e0d\u4f1a\u88ab\u653e\u5728\u4e00\u8d77\u3002\u4f8b\u5982\uff0cAnnie Hall\u548cCitizen Kane\u5c31\u9760\u5728\u4e00\u8d77\u3002\u5c3d\u7ba1\u5b83\u4eec\u5728\u98ce\u683c\u4e0a\u975e\u5e38\u4e0d\u540c\uff0c\u4f46\u5b83\u4eec\u4f5c\u4e3a\u5907\u53d7\u63a8\u5d07\u7684\u7ecf\u5178\u7535\u5f71\uff0c\u7531\u77e5\u540d\u5bfc\u6f14\u6267\u5bfc\uff0c\u6709\u5f88\u591a\u5171\u540c\u4e4b\u5904\u3002\u4e8b\u5b9e\u4e0a\uff0c\u56e0\u5b50\u5206\u89e3\u4e2d\u7684\u7b2c\u4e09\u4e2a\u7ef4\u5ea6\u786e\u5b9e\u5c06\u5b83\u4eec\u5206\u5f00\u3002<\/p>\n<p>\u6211\u4eec\u5c1d\u8bd5\u4e86\u8bb8\u591a\u4e0d\u540c\u7684\u56e0\u5b50\u5206\u89e3\u5b9e\u73b0\u548c\u53c2\u6570\u5316\u65b9\u6cd5\u3002\u56fe4\u5c55\u793a\u4e86\u4e0d\u540c\u6a21\u578b\u548c\u53c2\u6570\u6570\u91cf\u5982\u4f55\u5f71\u54cd\u5747\u65b9\u6839\u8bef\u5dee\uff08RMSE\uff09\uff0c\u4ee5\u53ca\u56e0\u5b50\u5206\u89e3\u4e0d\u540c\u5b9e\u73b0\u7684\u6027\u80fd\uff0c\u5305\u62ec\u7b80\u5355\u7684\u56e0\u5b50\u5206\u89e3\u3001\u6dfb\u52a0\u504f\u5dee\u3001\u4f7f\u7528\u9690\u6027\u53cd\u9988\u589e\u5f3a\u7528\u6237\u914d\u7f6e\u6587\u4ef6\uff0c\u4ee5\u53ca\u4e24\u79cd\u6dfb\u52a0\u65f6\u95f4\u6210\u5206\u7684\u53d8\u4f53\u3002\u6bcf\u4e2a\u56e0\u5b50\u6a21\u578b\u7684\u51c6\u786e\u6027\u90fd\u968f\u7740\u6d89\u53ca\u7684\u53c2\u6570\u6570\u91cf\u589e\u52a0\u800c\u63d0\u9ad8\uff0c\u8fd9\u7b49\u6548\u4e8e\u589e\u52a0\u56e0\u5b50\u6a21\u578b\u7684\u7ef4\u5ea6\uff0c\u56fe\u8868\u4e2d\u7684\u6570\u5b57\u8868\u793a\u7ef4\u5ea6\u7684\u5927\u5c0f\u3002<\/p>\n<p>\u66f4\u590d\u6742\u7684\u56e0\u5b50\u6a21\u578b\uff0c\u5176\u63cf\u8ff0\u6d89\u53ca\u66f4\u591a\u4e0d\u540c\u7684\u53c2\u6570\u96c6\uff0c\u66f4\u51c6\u786e\u3002\u4e8b\u5b9e\u4e0a\uff0c\u65f6\u95f4\u6210\u5206\u7279\u522b\u91cd\u8981\uff0c\u56e0\u4e3a\u6570\u636e\u4e2d\u5b58\u5728\u663e\u8457\u7684\u65f6\u95f4\u6548\u5e94\u3002<\/p>\n<p>\u77e9\u9635\u5206\u89e3\u6280\u672f\u5df2\u6210\u4e3a\u534f\u540c\u8fc7\u6ee4\u63a8\u8350\u7cfb\u7edf\u4e2d\u4e3b\u8981\u7684\u65b9\u6cd5\u5b66\u3002\u5bf9Netflix Prize\u6570\u636e\u7b49\u6570\u636e\u96c6\u7684\u7ecf\u9a8c\u8868\u660e\uff0c\u5b83\u4eec\u63d0\u4f9b\u6bd4\u4f20\u7edf\u6700\u8fd1\u90bb\u6280\u672f\u66f4\u9ad8\u7684\u51c6\u786e\u6027\u3002\u540c\u65f6\uff0c\u5b83\u4eec\u63d0\u4f9b\u4e86\u4e00\u79cd\u7d27\u51d1\u7684\u3001\u5185\u5b58\u9ad8\u6548\u7684\u6a21\u578b\uff0c\u7cfb\u7edf\u53ef\u4ee5\u76f8\u5bf9\u5bb9\u6613\u5730\u8fdb\u884c\u5b66\u4e60\u3002\u66f4\u65b9\u4fbf\u7684\u662f\uff0c\u8fd9\u4e9b\u6280\u672f\u8fd8\u53ef\u4ee5\u81ea\u7136\u5730\u96c6\u6210\u8bb8\u591a\u5173\u952e\u7684\u6570\u636e\u65b9\u9762\uff0c\u5982\u591a\u79cd\u5f62\u5f0f\u7684\u53cd\u9988\u3001\u65f6\u95f4\u52a8\u6001\u548c\u7f6e\u4fe1\u5ea6\u6c34\u5e73\u3002<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/106.52.213.145:21080\/wp-content\/uploads\/2023\/06\/\u622a\u5716-2023-06-29-\u4e0a\u534812.36.35-1024x915.png\" alt=\"\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u77e9\u9635\u5206\u89e3\u6280\u672f\u7528\u4e8e\u63a8\u8350\u7cfb\u7edf Yehuda Koren, Yahoo Research Robert Bell a&#8230; &raquo; <a class=\"read-more-link\" href=\"https:\/\/apifj.com\/index.php\/2023\/06\/13\/lunwenyuedumatrix-factorization-techniques-for-recommender-systems\/\">\u9605\u8bfb\u5168\u6587<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,7],"tags":[],"class_list":["post-216","post","type-post","status-publish","format-standard","hentry","category-dl","category-xuexibiji"],"_links":{"self":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/216","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/comments?post=216"}],"version-history":[{"count":7,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/216\/revisions"}],"predecessor-version":[{"id":227,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/216\/revisions\/227"}],"wp:attachment":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/media?parent=216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/categories?post=216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/tags?post=216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}