{"id":190,"date":"2023-06-09T09:12:33","date_gmt":"2023-06-09T01:12:33","guid":{"rendered":"http:\/\/106.52.213.145:21080\/?p=190"},"modified":"2023-06-29T00:40:46","modified_gmt":"2023-06-28T16:40:46","slug":"xuexibijijuzhenfenjie","status":"publish","type":"post","link":"https:\/\/apifj.com\/index.php\/2023\/06\/09\/xuexibijijuzhenfenjie\/","title":{"rendered":"[\u5b66\u4e60\u7b14\u8bb0]\u77e9\u9635\u5206\u89e3"},"content":{"rendered":"<h1>\u77e9\u9635\u5206\u89e3<\/h1>\n<p><img decoding=\"async\" src=\"http:\/\/106.52.213.145:21080\/wp-content\/uploads\/2023\/06\/\u622a\u5716-2023-06-09-\u4e0a\u53489.09.52-1024x340.png\" alt=\"\" \/><\/p>\n<p>\u63a8\u8350\u7b97\u6cd5\u8981\u9884\u6d4b\u7528\u6237\u6240\u6ca1\u6709\u770b\u8fc7\u7684\u4e1c\u897f\u7684\u8bc4\u5206\uff0c\u4e3a\u4e86\u80fd\u591f\u9884\u6d4b\u7528\u6237\u7684\u8bc4\u5206\uff0c\u6211\u4eec\u9700\u8981\u6784\u5efa\u4e24\u4e2a\u77e9\u9635U\u3001V\uff0c\u901a\u8fc7\u6784\u5efa\u7684\u4e24\u4e2a\u77e9\u9635U\u3001V\u6765\u9884\u6d4bUser-Item\u77e9\u9635\u7684\u7a7a\u7f3a\u90e8\u5206\uff0c\u4e5f\u5c31\u662f\u77e9\u9635R\u4e2d\u7a7a\u7684\u3002\u5176\u4e2dU\u3001V\u5206\u522b\u4ee3\u8868\u7528\u6237\u3001\u7269\u54c1\u7684\u7279\u5f81(feature)\uff0c\u901a\u8fc7\u67d0\u4e00\u4e2a\u7528\u6237\u7684\u5411\u91cf\u4e0e\u67d0\u4e00\u4e2a\u7269\u54c1\u5411\u91cf\u505a\u5185\u79ef\u4ece\u800c\u5f97\u51fa\u8be5\u7528\u6237\u5bf9\u8fd9\u4e2a\u7269\u54c1\u7684\u504f\u597d\u7a0b\u5ea6\u3002\u800c\u6838\u5fc3\u95ee\u9898\u5c31\u8f6c\u5316\u5230\u4e86\u6211\u4eec\u5982\u4f55\u6784\u5efa\u4e00\u4e2aU\u548cV\u6765\u80fd\u591f\u6700\u5927\u7a0b\u5ea6\u62df\u5408\u7528\u6237\u4e4b\u7279\u5f81\u3002<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/106.52.213.145:21080\/wp-content\/uploads\/2023\/06\/\u622a\u5716-2023-06-09-\u4e0a\u53489.10.30-1024x409.png\" alt=\"\" \/><br \/>\n\u5bf9\u4e8e\u5982\u4e0a\u56fe\uff0c\u77e9\u9635\u5206\u89e3\u7b97\u6cd5\u5c06<code class=\"mathjax-inline language-mathjax\">m \\times n<\/code> \u7ef4\u7684\u77e9\u9635R\u5206\u89e3\u4e3a<code class=\"mathjax-inline language-mathjax\">m \\times k<\/code>\u7684\u7528\u6237\u77e9\u9635P\u548c <code class=\"mathjax-inline language-mathjax\">k \\times n<\/code>\u7ef4\u7684\u7269\u54c1\u77e9\u9635Q\u76f8\u4e58\u7684\u5f62\u5f0f\u3002\u5176\u4e2dm\u4e3a\u7528\u6237\u7684\u6570\u91cf\uff0c n\u4e3a\u7269\u54c1\u7684\u6570\u91cf\uff0ck\u4e3a\u9690\u5411\u91cf\uff08Latent Factor\uff09\u7684\u7ef4\u5ea6\u3002 k\u662f\u8d85\u53c2\u6570\u3002<\/p>\n<p>\u5c06\u4e24\u4e2a\u77e9\u9635\u76f8\u4e58\uff0c\u5c31\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u6ee1\u79e9\u7684\u77e9\u9635R\u3002\u90a3\u4e48\uff0c\u6211\u4eec\u5c31\u5bf9\u672a\u88ab\u8bc4\u4ef7\u8fc7\u7684\u7269\u54c1\uff0c\u6709\u4e86\u4e00\u4e2a\u9884\u6d4b\u8bc4\u5206\u3002\u63a5\u4e0b\u6765\uff0c\u53ef\u4ee5\u5c06\u8bc4\u5206\u8fdb\u884c\u6392\u5e8f\uff0c\u63a8\u8350\u7ed9\u7528\u6237\u3002\u8fd9\u5c31\u662f\u77e9\u9635\u5206\u89e3\u5bf9\u4e8e\u63a8\u8350\u7cfb\u7edf\u6700\u57fa\u672c\u7684\u7528\u9014\u3002\u77e9\u9635R\u7b2cu\u884c\u7b2ci\u5217\u7684\u5143\u7d20\uff0c\u53ef\u4ee5\u8868\u793a\u7b2cu\u4e2a\u4eba\u5bf9\u7b2ci\u4e2aitem\u7684\u5174\u8da3\u7a0b\u5ea6\u3002<\/p>\n<p>\u5c06\u73b0\u6709\u7684\u7a00\u758f\u77e9\u9635R\u5206\u89e3\u4e3a\u4e24\u4e2a\u77e9\u9635\uff0ck\u4e3a\u9690\u5411\u91cf\uff0ck\u7684\u957f\u5ea6\u662f\u6240\u9009\u53d6\u7684\u7279\u5f81\u957f\u5ea6\uff0c\u4e5f\u662f\u4e00\u4e2a\u8d85\u53c2\u6570\u3002\u5728\u5206\u89e3\u5b8c\u6210\u4e24\u4e2a\u77e9\u9635\u540e\uff0c\u6211\u4eec\u5c31\u9700\u8981\u5b66\u4e60U\u548cV\u7684k\u5411\u91cf\uff0c\u8ba9\u4ed6\u66f4\u597d\u7684\u5339\u914dR\u77e9\u9635\u3002<\/p>\n<p><strong><strong>\u77e9\u9635\u5206\u89e3\u7684\u76ee\u7684<\/strong><\/strong>: \u901a\u8fc7\u5206\u89e3\u4e4b\u540e\u7684\u4e24\u77e9\u9635\u5185\u79ef\uff0c\u6765\u586b\u8865\u7f3a\u5931\u7684\u6570\u636e\uff0c\u7528\u6765\u505a\u9884\u6d4b\u8bc4\u5206\u3002 \u901a\u8fc7\u673a\u5668\u5b66\u4e60\u7684\u624b\u6bb5\u5c06\u7528\u6237\u884c\u4e3a\u77e9\u9635\u4e2d\u7f3a\u5931\u7684\u6570\u636e(\u7528\u6237\u6ca1\u6709\u8bc4\u5206\u7684\u5143\u7d20)\u586b\u8865\u5b8c\u6574\uff0c\u6700\u7ec8\u8fbe\u5230\u53ef\u4ee5\u4e3a\u7528\u6237\u505a\u63a8\u8350\u7684\u76ee\u6807\u3002<\/p>\n<h2>\u7279\u5f81\u503c\u5206\u89e3<\/h2>\n<p>A\u4e3an\u9636\u77e9\u9635\uff0c\u6709\u5982\u4e0b\u516c\u5f0f<\/p>\n<pre><code class=\"language-mathjax\">A\\alpha = \\lambda \\alpha<\/code><\/pre>\n<p>\u5219<code class=\"mathjax-inline language-mathjax\">\\alpha<\/code> \u662f\u7279\u5f81\u5411\u91cf\u3001<code class=\"mathjax-inline language-mathjax\">\\lambda<\/code> \u662f\u7279\u5f81\u503c<\/p>\n<p>\u4e8e\u662f\u6211\u4eec\u6709<\/p>\n<pre><code class=\"language-mathjax\">A=Q\u03a3Q<\/code><\/pre>\n<p>Q\u662f\u7279\u5f81\u5411\u91cf\u3002\u03a3\u662f\u5bf9\u89d2\u77e9\u9635\uff0c\u5bf9\u89d2\u7ebf\u4e0a\u662f\u77e9\u9635A\u7684\u7531\u5927\u5230\u5c0f\u6392\u5217\u7684\u7279\u5f81\u503c\uff0c\u4ed6\u4eec\u987a\u5e8f\u4ee3\u8868\u7740\u5bf9\u77e9\u9635Q\u53d8\u5316\u65b9\u5411\u7684\u91cd\u8981\u7a0b\u5ea6\uff0c\u5229\u7528\u524dN\u4e2a\u503c\u5c31\u53ef\u4ee5\u5f97\u5230\u63a5\u8fd1\u8fd9\u4e2a\u77e9\u9635\u7684\u53d8\u5316\uff0c\u4ece\u800c\u63d0\u53d6\u8fd9\u4e2a\u77e9\u9635\u6700\u91cd\u8981\u7684\u7279\u5f81\uff0c\u6bd4\u5982\u4e0b\u9762\u7684\u8003\u7814\u5178\u578b\u9898\u76ee\uff1a<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/106.52.213.145:21080\/wp-content\/uploads\/2023\/06\/\u622a\u5716-2023-06-09-\u4e0a\u53484.12.01-739x1024.png\" alt=\"\" \/><\/p>\n<h2>\u5947\u5f02\u503c\u5206\u89e3<\/h2>\n<p>\u5bf9\u4e8e\u4e00\u4e2a<code class=\"mathjax-inline language-mathjax\">m \\times n<\/code>\u77e9\u9635<code class=\"mathjax-inline language-mathjax\">M<\/code>\uff0c\u6709<\/p>\n<pre><code class=\"language-mathjax\">M=U\u03a3V^T<\/code><\/pre>\n<p>\u5176\u4e2d U\u662f<code class=\"mathjax-inline language-mathjax\">m \\times n<\/code>\u7684\u6b63\u4ea4\u77e9\u9635\uff0c V \u662f <code class=\"mathjax-inline language-mathjax\">n \\times n<\/code>\u7684\u6b63\u4ea4\u77e9\u9635\uff0c  <code class=\"mathjax-inline language-mathjax\">\\Sigma<\/code>\u662f<code class=\"mathjax-inline language-mathjax\">m \\times n<\/code>\u7684\u5bf9\u89d2\u77e9\u9635\u3002 \u03a3\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u5c31\u79f0\u4e3aM\u7684\u5947\u5f02\u503c.<\/p>\n<p>\u5206\u89e3\u540e\uff0c U\u77e9\u9635\u4e3a<code class=\"mathjax-inline language-mathjax\">6 \\times 6<\/code>\u7684\u6b63\u4ea4\u77e9\u9635, V\u4e3a<code class=\"mathjax-inline language-mathjax\">4 \\times 4<\/code>\u7684\u6b63\u4ea4\u77e9\u9635\u3002 S\u4e3a\u5bf9\u89d2\u77e9\u9635\u5373\u516c\u5f0f\u4e2d\u7684<code class=\"mathjax-inline language-mathjax\">\\Sigma<\/code>\u3002\u9009\u53d6S\u4e2d\u8f83\u5927\u7684k\u4e2a\u5143\u7d20\u4f5c\u4e3a\u9690\u542b\u7279\u5f81\u3002\u5220\u9664S\u7684\u5176\u4ed6\u7ef4\u5ea6\u4ee5\u53ca U\u548c V\u5bf9\u5e94\u7684\u7ef4\u5ea6\uff0c\u77e9\u9635\u5206\u89e3\u5c31\u5b8c\u6210\u4e86\u3002<\/p>\n<h2>Funk-SVD<\/h2>\n<p>\u76f4\u63a5\u901a\u8fc7\u8bad\u7ec3\u96c6\u4e2d\u7684\u89c2\u5bdf\u503c\u5229\u7528\u6700\u5c0f\u5316RMSE\u5b66\u4e60\u7528\u6237\u7279\u5f81\u77e9\u9635P\u548c\u7269\u54c1\u7279\u5f81\u77e9\u9635Q\uff0c\u6316\u6398\u7528\u6237\u7684\u6f5c\u5728\u7279\u5f81\u77e9\u9635P\u548c\u7269\u54c1\u6f5c\u5728\u7279\u5f81\u77e9\u9635Q\u6765\u4f30\u8ba1\u8bc4\u5206<\/p>\n<pre><code class=\"language-mathjax\">R\u2248P \\times Q <\/code><\/pre>\n<p>\u5728\u6c42\u51fa\u4e86P\u3001Q\u540e\uff0c\u6211\u4eec\u5219\u6709<\/p>\n<pre><code class=\"language-mathjax\">r_{ij}=p_iq_j^T=\\sum_{k=1}^K p_{ik}q_{kj}<\/code><\/pre>\n<p>\u6240\u4ee5\u4f18\u5316\u76ee\u6807\u4e3a<\/p>\n<pre><code class=\"language-mathjax\">argmin \\sum_{i,j}(r_{ij}-p_iq_j)^2+(||p_i||+||q_j||)<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u77e9\u9635\u5206\u89e3 \u63a8\u8350\u7b97\u6cd5\u8981\u9884\u6d4b\u7528\u6237\u6240\u6ca1\u6709\u770b\u8fc7\u7684\u4e1c\u897f\u7684\u8bc4\u5206\uff0c\u4e3a\u4e86\u80fd\u591f\u9884\u6d4b\u7528\u6237\u7684\u8bc4\u5206\uff0c\u6211\u4eec\u9700\u8981\u6784\u5efa\u4e24\u4e2a\u77e9\u9635U\u3001V\uff0c\u901a\u8fc7\u6784&#8230; &raquo; <a class=\"read-more-link\" href=\"https:\/\/apifj.com\/index.php\/2023\/06\/09\/xuexibijijuzhenfenjie\/\">\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-190","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\/190","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=190"}],"version-history":[{"count":5,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/190\/revisions"}],"predecessor-version":[{"id":228,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/190\/revisions\/228"}],"wp:attachment":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/media?parent=190"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/categories?post=190"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/tags?post=190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}