{"id":478216,"date":"2023-08-09T09:29:10","date_gmt":"2023-08-09T09:29:10","guid":{"rendered":""},"modified":"2023-09-05T11:16:18","modified_gmt":"2023-09-05T11:16:18","slug":"non-negative-matrix-factorization-nmf","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/cn\/wiki\/non-negative-matrix-factorization-nmf\/","title":{"rendered":"\u975e\u8d1f\u77e9\u9635\u5206\u89e3 (NMF)"},"content":{"rendered":"<p>\u975e\u8d1f\u77e9\u9635\u5206\u89e3 (NMF) \u662f\u4e00\u79cd\u5f3a\u5927\u7684\u6570\u5b66\u6280\u672f\uff0c\u53ef\u7528\u4e8e\u6570\u636e\u5206\u6790\u3001\u7279\u5f81\u63d0\u53d6\u548c\u964d\u7ef4\u3002\u5b83\u5e7f\u6cdb\u5e94\u7528\u4e8e\u4fe1\u53f7\u5904\u7406\u3001\u56fe\u50cf\u5904\u7406\u3001\u6587\u672c\u6316\u6398\u3001\u751f\u7269\u4fe1\u606f\u5b66\u7b49\u5404\u4e2a\u9886\u57df\u3002NMF \u5141\u8bb8\u5c06\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u4e3a\u4e24\u4e2a\u6216\u591a\u4e2a\u975e\u8d1f\u77e9\u9635\uff0c\u8fd9\u4e9b\u77e9\u9635\u53ef\u4ee5\u89e3\u91ca\u4e3a\u57fa\u5411\u91cf\u548c\u7cfb\u6570\u3002\u8fd9\u79cd\u5206\u89e3\u5728\u5904\u7406\u975e\u8d1f\u6570\u636e\u65f6\u7279\u522b\u6709\u7528\uff0c\u56e0\u4e3a\u8d1f\u503c\u5728\u95ee\u9898\u80cc\u666f\u4e0b\u6ca1\u6709\u610f\u4e49\u3002<\/p>\n<h2>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff08NMF\uff09\u7684\u8d77\u6e90\u5386\u53f2\u53ca\u5176\u9996\u6b21\u63d0\u53ca\u3002<\/h2>\n<p>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u7684\u8d77\u6e90\u53ef\u4ee5\u8ffd\u6eaf\u5230 20 \u4e16\u7eaa 90 \u5e74\u4ee3\u521d\u3002\u5206\u89e3\u975e\u8d1f\u6570\u636e\u77e9\u9635\u7684\u6982\u5ff5\u53ef\u4ee5\u4e0e Paul Paatero \u548c Unto Tapper \u7684\u5de5\u4f5c\u8054\u7cfb\u8d77\u6765\uff0c\u4ed6\u4eec\u5728 1994 \u5e74\u53d1\u8868\u7684\u8bba\u6587\u4e2d\u5f15\u5165\u4e86\u201c\u6b63\u77e9\u9635\u5206\u89e3\u201d\u7684\u6982\u5ff5\u3002\u7136\u800c\uff0c\u201c\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u201d\u4e00\u8bcd\u53ca\u5176\u5177\u4f53\u7684\u7b97\u6cd5\u516c\u5f0f\u540e\u6765\u624d\u6d41\u884c\u8d77\u6765\u3002<\/p>\n<p>1999 \u5e74\uff0c\u7814\u7a76\u4eba\u5458 Daniel D. Lee \u548c H. Sebastian Seung \u5728\u4ed6\u4eec\u7684\u5f00\u521b\u6027\u8bba\u6587\u300a\u901a\u8fc7\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u5b66\u4e60\u7269\u4f53\u7684\u5404\u4e2a\u90e8\u5206\u300b\u4e2d\u63d0\u51fa\u4e86\u4e00\u79cd\u9488\u5bf9 NMF \u7684\u5177\u4f53\u7b97\u6cd5\u3002\u4ed6\u4eec\u7684\u7b97\u6cd5\u4e13\u6ce8\u4e8e\u975e\u8d1f\u7ea6\u675f\uff0c\u5141\u8bb8\u57fa\u4e8e\u5404\u4e2a\u90e8\u5206\u7684\u8868\u793a\u548c\u964d\u7ef4\u3002\u4ece\u90a3\u65f6\u8d77\uff0cNMF \u5f97\u5230\u4e86\u5e7f\u6cdb\u7684\u7814\u7a76\uff0c\u5e76\u5e94\u7528\u4e8e\u5404\u4e2a\u9886\u57df\u3002<\/p>\n<h2>\u6709\u5173\u975e\u8d1f\u77e9\u9635\u5206\u89e3 (NMF) \u7684\u8be6\u7ec6\u4fe1\u606f<\/h2>\n<p>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u7684\u539f\u7406\u662f\u4f7f\u7528\u4e24\u4e2a\u975e\u8d1f\u77e9\u9635\u201cW\u201d\u548c\u201cH\u201d\u6765\u8fd1\u4f3c\u975e\u8d1f\u6570\u636e\u77e9\u9635\uff08\u901a\u5e38\u8868\u793a\u4e3a\u201cV\u201d\uff09\u3002\u76ee\u6807\u662f\u627e\u5230\u8fd9\u4e9b\u77e9\u9635\uff0c\u4f7f\u5f97\u5b83\u4eec\u7684\u4e58\u79ef\u8fd1\u4f3c\u4e8e\u539f\u59cb\u77e9\u9635\uff1a<\/p>\n<p>V\u2248WH<\/p>\n<p>\u5728\u54ea\u91cc\uff1a<\/p>\n<ul>\n<li>V \u662f\u5927\u5c0f\u4e3a mxn \u7684\u539f\u59cb\u6570\u636e\u77e9\u9635<\/li>\n<li>W \u662f\u5927\u5c0f\u4e3a mxk \u7684\u57fa\u77e9\u9635\uff08\u5176\u4e2d k \u662f\u6240\u9700\u7684\u57fa\u5411\u91cf\u6216\u5206\u91cf\u7684\u6570\u91cf\uff09<\/li>\n<li>H \u662f\u5927\u5c0f\u4e3a kxn \u7684\u7cfb\u6570\u77e9\u9635<\/li>\n<\/ul>\n<p>\u56e0\u5f0f\u5206\u89e3\u5e76\u4e0d\u552f\u4e00\uff0c\u5e76\u4e14\u53ef\u4ee5\u6839\u636e\u6240\u9700\u7684\u8fd1\u4f3c\u7ea7\u522b\u8c03\u6574 W \u548c H \u7684\u5c3a\u5bf8\u3002NMF \u901a\u5e38\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u3001\u4ea4\u66ff\u6700\u5c0f\u4e8c\u4e58\u6216\u4e58\u6cd5\u66f4\u65b0\u7b49\u4f18\u5316\u6280\u672f\u6765\u5b9e\u73b0\uff0c\u4ee5\u6700\u5c0f\u5316 V \u548c WH \u4e4b\u95f4\u7684\u8bef\u5dee\u3002<\/p>\n<h2>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff08NMF\uff09\u7684\u5185\u90e8\u7ed3\u6784\u3002\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff08NMF\uff09\u7684\u5de5\u4f5c\u539f\u7406\u3002<\/h2>\n<p>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5206\u89e3\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u7684\u5185\u90e8\u7ed3\u6784\u53ca\u5176\u8fd0\u7b97\u7684\u57fa\u672c\u539f\u7406\u6765\u7406\u89e3\u5b83\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u975e\u8d1f\u6027\u7ea6\u675f\uff1a<\/strong> NMF \u5bf9\u57fa\u77e9\u9635 W \u548c\u7cfb\u6570\u77e9\u9635 H \u90fd\u5f3a\u5236\u5b9e\u65bd\u975e\u8d1f\u7ea6\u675f\u3002\u6b64\u7ea6\u675f\u81f3\u5173\u91cd\u8981\uff0c\u56e0\u4e3a\u5b83\u5141\u8bb8\u751f\u6210\u7684\u57fa\u5411\u91cf\u548c\u7cfb\u6570\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u5177\u6709\u53ef\u52a0\u6027\u4e14\u53ef\u89e3\u91ca\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7279\u5f81\u63d0\u53d6\u548c\u964d\u7ef4\uff1a<\/strong> NMF \u901a\u8fc7\u8bc6\u522b\u6570\u636e\u4e2d\u6700\u76f8\u5173\u7684\u7279\u5f81\u5e76\u5c06\u5176\u8868\u793a\u5728\u8f83\u4f4e\u7ef4\u7a7a\u95f4\u4e2d\u6765\u5b9e\u73b0\u7279\u5f81\u63d0\u53d6\u3002\u8fd9\u79cd\u964d\u7ef4\u5728\u5904\u7406\u9ad8\u7ef4\u6570\u636e\u65f6\u5c24\u5176\u6709\u4ef7\u503c\uff0c\u56e0\u4e3a\u5b83\u7b80\u5316\u4e86\u6570\u636e\u8868\u793a\uff0c\u5e76\u4e14\u901a\u5e38\u53ef\u4ee5\u4ea7\u751f\u66f4\u6613\u4e8e\u89e3\u91ca\u7684\u7ed3\u679c\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u57fa\u4e8e\u90e8\u4ef6\u7684\u8868\u793a\uff1a<\/strong> NMF \u7684\u4e00\u4e2a\u5173\u952e\u4f18\u52bf\u662f\u5b83\u80fd\u591f\u63d0\u4f9b\u539f\u59cb\u6570\u636e\u7684\u57fa\u4e8e\u90e8\u5206\u7684\u8868\u793a\u3002\u8fd9\u610f\u5473\u7740 W \u4e2d\u7684\u6bcf\u4e2a\u57fa\u5411\u91cf\u5bf9\u5e94\u4e8e\u6570\u636e\u4e2d\u7684\u7279\u5b9a\u7279\u5f81\u6216\u6a21\u5f0f\uff0c\u800c\u7cfb\u6570\u77e9\u9635 H \u8868\u793a\u8fd9\u4e9b\u7279\u5f81\u5728\u6bcf\u4e2a\u6570\u636e\u6837\u672c\u4e2d\u7684\u5b58\u5728\u548c\u76f8\u5173\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6570\u636e\u538b\u7f29\u548c\u53bb\u566a\u4e2d\u7684\u5e94\u7528\uff1a<\/strong> NMF \u53ef\u7528\u4e8e\u6570\u636e\u538b\u7f29\u548c\u53bb\u566a\u3002\u901a\u8fc7\u4f7f\u7528\u8f83\u5c11\u6570\u91cf\u7684\u57fa\u5411\u91cf\uff0c\u53ef\u4ee5\u8fd1\u4f3c\u539f\u59cb\u6570\u636e\uff0c\u540c\u65f6\u964d\u4f4e\u5176\u7ef4\u6570\u3002\u8fd9\u53ef\u4ee5\u5b9e\u73b0\u9ad8\u6548\u5b58\u50a8\u548c\u66f4\u5feb\u5904\u7406\u5927\u578b\u6570\u636e\u96c6\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff08NMF\uff09\u7684\u5173\u952e\u7279\u5f81\u5206\u6790<\/h2>\n<p>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u7684\u4e3b\u8981\u7279\u5f81\u53ef\u4ee5\u6982\u62ec\u5982\u4e0b\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u975e\u8d1f\u6027\uff1a<\/strong> NMF \u5bf9\u57fa\u77e9\u9635\u548c\u7cfb\u6570\u77e9\u9635\u90fd\u5f3a\u5236\u975e\u8d1f\u7ea6\u675f\uff0c\u4f7f\u5176\u9002\u7528\u4e8e\u8d1f\u503c\u6ca1\u6709\u6709\u610f\u4e49\u89e3\u91ca\u7684\u6570\u636e\u96c6\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u57fa\u4e8e\u90e8\u4ef6\u7684\u8868\u793a\uff1a<\/strong> NMF \u63d0\u4f9b\u4e86\u57fa\u4e8e\u90e8\u5206\u7684\u6570\u636e\u8868\u793a\uff0c\u4f7f\u5176\u53ef\u7528\u4e8e\u4ece\u6570\u636e\u4e2d\u63d0\u53d6\u6709\u610f\u4e49\u7684\u7279\u5f81\u548c\u6a21\u5f0f\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u964d\u7ef4\uff1a<\/strong> NMF\u6709\u52a9\u4e8e\u964d\u4f4e\u7ef4\u6570\uff0c\u4ece\u800c\u80fd\u591f\u6709\u6548\u5730\u5b58\u50a8\u548c\u5904\u7406\u9ad8\u7ef4\u6570\u636e\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u53ef\u89e3\u91ca\u6027\uff1a<\/strong> \u4ece NMF \u83b7\u5f97\u7684\u57fa\u5411\u91cf\u548c\u7cfb\u6570\u901a\u5e38\u662f\u53ef\u89e3\u91ca\u7684\uff0c\u4ece\u800c\u53ef\u4ee5\u5bf9\u5e95\u5c42\u6570\u636e\u63d0\u4f9b\u6709\u610f\u4e49\u7684\u89c1\u89e3\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u9c81\u68d2\u6027\uff1a<\/strong> NMF \u53ef\u4ee5\u6709\u6548\u5730\u5904\u7406\u7f3a\u5931\u6216\u4e0d\u5b8c\u6574\u7684\u6570\u636e\uff0c\u4f7f\u5176\u9002\u7528\u4e8e\u4e0d\u5b8c\u5584\u7684\u771f\u5b9e\u4e16\u754c\u6570\u636e\u96c6\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7075\u6d3b\u6027\uff1a<\/strong> NMF \u53ef\u4ee5\u9002\u5e94\u5404\u79cd\u4f18\u5316\u6280\u672f\uff0c\u5141\u8bb8\u6839\u636e\u7279\u5b9a\u6570\u636e\u7279\u5f81\u548c\u8981\u6c42\u8fdb\u884c\u5b9a\u5236\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u975e\u8d1f\u77e9\u9635\u5206\u89e3 (NMF) \u7684\u7c7b\u578b<\/h2>\n<p>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u6709\u51e0\u79cd\u53d8\u4f53\u548c\u6269\u5c55\uff0c\u6bcf\u79cd\u90fd\u6709\u81ea\u5df1\u7684\u4f18\u52bf\u548c\u5e94\u7528\u3002\u4e00\u4e9b\u5e38\u89c1\u7684 NMF \u7c7b\u578b\u5305\u62ec\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u7ecf\u5178 NMF\uff1a<\/strong> NMF \u7684\u539f\u59cb\u516c\u5f0f\u7531 Lee \u548c Seung \u63d0\u51fa\uff0c\u4f7f\u7528\u4e58\u6cd5\u66f4\u65b0\u6216\u4ea4\u66ff\u6700\u5c0f\u4e8c\u4e58\u7b49\u65b9\u6cd5\u8fdb\u884c\u4f18\u5316\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7a00\u758f NMF\uff1a<\/strong> \u8be5\u53d8\u4f53\u5f15\u5165\u4e86\u7a00\u758f\u6027\u7ea6\u675f\uff0c\u4ece\u800c\u4f7f\u5f97\u6570\u636e\u8868\u793a\u66f4\u52a0\u6613\u4e8e\u89e3\u91ca\u4e14\u66f4\u52a0\u9ad8\u6548\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7a33\u5065\u7684 NMF\uff1a<\/strong> \u7a33\u5065\u7684 NMF \u7b97\u6cd5\u65e8\u5728\u5904\u7406\u6570\u636e\u4e2d\u7684\u5f02\u5e38\u503c\u548c\u566a\u58f0\uff0c\u63d0\u4f9b\u66f4\u53ef\u9760\u7684\u5206\u89e3\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5206\u5c42 NMF\uff1a<\/strong> \u5728\u5206\u5c42 NMF \u4e2d\uff0c\u6267\u884c\u591a\u7ea7\u5206\u89e3\uff0c\u4ece\u800c\u5b9e\u73b0\u6570\u636e\u7684\u5206\u5c42\u8868\u793a\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6838 NMF\uff1a<\/strong> \u6838 NMF \u5c06 NMF \u7684\u6982\u5ff5\u6269\u5c55\u5230\u6838\u8bf1\u5bfc\u7684\u7279\u5f81\u7a7a\u95f4\uff0c\u4ece\u800c\u5b9e\u73b0\u4e86\u975e\u7ebf\u6027\u6570\u636e\u7684\u5206\u89e3\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u76d1\u7763 NMF\uff1a<\/strong> \u8be5\u53d8\u4f53\u5c06\u7c7b\u6807\u7b7e\u6216\u76ee\u6807\u4fe1\u606f\u7eb3\u5165\u5206\u89e3\u8fc7\u7a0b\uff0c\u4f7f\u5176\u9002\u5408\u5206\u7c7b\u4efb\u52a1\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u4e0b\u8868\u603b\u7ed3\u4e86\u4e0d\u540c\u7c7b\u578b\u7684\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u53ca\u5176\u7279\u5f81\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th>NMF \u7c7b\u578b<\/th>\n<th>\u7279\u5f81<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u7ecf\u5178 NMF<\/td>\n<td>\u5177\u6709\u975e\u8d1f\u7ea6\u675f\u7684\u539f\u59cb\u516c\u5f0f<\/td>\n<\/tr>\n<tr>\n<td>\u7a00\u758f NMF<\/td>\n<td>\u5f15\u5165\u7a00\u758f\u6027\u4ee5\u83b7\u5f97\u66f4\u6613\u4e8e\u89e3\u91ca\u7684\u7ed3\u679c<\/td>\n<\/tr>\n<tr>\n<td>\u7a33\u5065 NMF<\/td>\n<td>\u6709\u6548\u5904\u7406\u5f02\u5e38\u503c\u548c\u566a\u97f3<\/td>\n<\/tr>\n<tr>\n<td>\u5206\u5c42 NMF<\/td>\n<td>\u63d0\u4f9b\u6570\u636e\u7684\u5c42\u6b21\u5316\u8868\u793a<\/td>\n<\/tr>\n<tr>\n<td>\u6838 NMF<\/td>\n<td>\u5c06 NMF \u6269\u5c55\u81f3\u6838\u8bf1\u5bfc\u7279\u5f81\u7a7a\u95f4<\/td>\n<\/tr>\n<tr>\n<td>\u76d1\u7763 NMF<\/td>\n<td>\u7ed3\u5408\u7c7b\u522b\u6807\u7b7e\u8fdb\u884c\u5206\u7c7b\u4efb\u52a1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff08NMF\uff09\u7684\u4f7f\u7528\u65b9\u6cd5\u3001\u4f7f\u7528\u76f8\u5173\u7684\u95ee\u9898\u53ca\u5176\u89e3\u51b3\u65b9\u6848\u3002<\/h2>\n<p>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u5728\u5404\u4e2a\u9886\u57df\u90fd\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u4e0e NMF \u76f8\u5173\u7684\u4e00\u4e9b\u5e38\u89c1\u7528\u4f8b\u548c\u6311\u6218\u5982\u4e0b\uff1a<\/p>\n<h3>NMF \u7684\u7528\u4f8b\uff1a<\/h3>\n<ol>\n<li>\n<p><strong>\u56fe\u50cf\u5904\u7406\uff1a<\/strong> NMF \u5728\u56fe\u50cf\u5904\u7406\u5e94\u7528\u4e2d\u7528\u4e8e\u56fe\u50cf\u538b\u7f29\u3001\u53bb\u566a\u548c\u7279\u5f81\u63d0\u53d6\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6587\u672c\u6316\u6398\uff1a<\/strong> NMF \u6709\u52a9\u4e8e\u4e3b\u9898\u5efa\u6a21\u3001\u6587\u6863\u805a\u7c7b\u548c\u6587\u672c\u6570\u636e\u7684\u60c5\u611f\u5206\u6790\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u751f\u7269\u4fe1\u606f\u5b66\uff1a<\/strong> NMF \u7528\u4e8e\u57fa\u56e0\u8868\u8fbe\u5206\u6790\u3001\u8bc6\u522b\u751f\u7269\u6570\u636e\u4e2d\u7684\u6a21\u5f0f\u548c\u836f\u7269\u53d1\u73b0\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u97f3\u9891\u4fe1\u53f7\u5904\u7406\uff1a<\/strong> NMF\u7528\u4e8e\u6e90\u5206\u79bb\u548c\u97f3\u4e50\u5206\u6790\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u63a8\u8350\u7cfb\u7edf\uff1a<\/strong> NMF \u53ef\u7528\u4e8e\u901a\u8fc7\u8bc6\u522b\u7528\u6237\u4e0e\u5546\u54c1\u4ea4\u4e92\u4e2d\u7684\u6f5c\u5728\u56e0\u7d20\u6765\u6784\u5efa\u4e2a\u6027\u5316\u63a8\u8350\u7cfb\u7edf\u3002<\/p>\n<\/li>\n<\/ol>\n<h3>\u6311\u6218\u548c\u89e3\u51b3\u65b9\u6848\uff1a<\/h3>\n<ol>\n<li>\n<p><strong>\u521d\u59cb\u5316\uff1a<\/strong> NMF \u5bf9 W \u548c H \u7684\u521d\u59cb\u503c\u7684\u9009\u62e9\u5f88\u654f\u611f\u3002\u5404\u79cd\u521d\u59cb\u5316\u7b56\u7565\uff08\u5982\u968f\u673a\u521d\u59cb\u5316\u6216\u4f7f\u7528\u5176\u4ed6\u964d\u7ef4\u6280\u672f\uff09\u53ef\u4ee5\u5e2e\u52a9\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5206\u6b67\uff1a<\/strong> NMF \u4e2d\u4f7f\u7528\u7684\u67d0\u4e9b\u4f18\u5316\u65b9\u6cd5\u53ef\u80fd\u4f1a\u51fa\u73b0\u53d1\u6563\u95ee\u9898\uff0c\u5bfc\u81f4\u6536\u655b\u901f\u5ea6\u6162\u6216\u9677\u5165\u5c40\u90e8\u6700\u4f18\u3002\u4f7f\u7528\u9002\u5f53\u7684\u66f4\u65b0\u89c4\u5219\u548c\u6b63\u5219\u5316\u6280\u672f\u53ef\u4ee5\u7f13\u89e3\u6b64\u95ee\u9898\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u8fc7\u62df\u5408\uff1a<\/strong> \u4f7f\u7528 NMF \u8fdb\u884c\u7279\u5f81\u63d0\u53d6\u65f6\uff0c\u5b58\u5728\u6570\u636e\u8fc7\u5ea6\u62df\u5408\u7684\u98ce\u9669\u3002\u6b63\u5219\u5316\u548c\u4ea4\u53c9\u9a8c\u8bc1\u7b49\u6280\u672f\u53ef\u4ee5\u5e2e\u52a9\u9632\u6b62\u8fc7\u5ea6\u62df\u5408\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6570\u636e\u7f29\u653e\uff1a<\/strong> NMF \u5bf9\u8f93\u5165\u6570\u636e\u7684\u5c3a\u5ea6\u5f88\u654f\u611f\u3002\u5728\u5e94\u7528 NMF \u4e4b\u524d\u9002\u5f53\u7f29\u653e\u6570\u636e\u53ef\u4ee5\u63d0\u9ad8\u5176\u6027\u80fd\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7f3a\u5931\u6570\u636e\uff1a<\/strong> NMF \u7b97\u6cd5\u53ef\u4ee5\u5904\u7406\u7f3a\u5931\u6570\u636e\uff0c\u4f46\u8fc7\u591a\u7684\u7f3a\u5931\u503c\u4f1a\u5bfc\u81f4\u56e0\u5f0f\u5206\u89e3\u4e0d\u51c6\u786e\u3002\u53ef\u4ee5\u4f7f\u7528\u63d2\u8865\u6280\u672f\u6765\u6709\u6548\u5904\u7406\u7f3a\u5931\u6570\u636e\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u4ee5\u8868\u683c\u548c\u5217\u8868\u7684\u5f62\u5f0f\u5217\u51fa\u4e3b\u8981\u7279\u5f81\u4ee5\u53ca\u4e0e\u7c7b\u4f3c\u672f\u8bed\u7684\u5176\u4ed6\u6bd4\u8f83\u3002<\/h2>\n<p>\u4e0b\u9762\u662f\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u4e0e\u5176\u4ed6\u7c7b\u4f3c\u6280\u672f\u7684\u6bd4\u8f83\u8868\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th>\u6280\u672f<\/th>\n<th>\u975e\u8d1f\u6027\u7ea6\u675f<\/th>\n<th>\u53ef\u89e3\u91ca\u6027<\/th>\n<th>\u7a00\u758f\u6027<\/th>\n<th>\u5904\u7406\u7f3a\u5931\u6570\u636e<\/th>\n<th>\u7ebf\u6027\u5047\u8bbe<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u975e\u8d1f\u77e9\u9635\u5206\u89e3 (NMF)<\/td>\n<td>\u662f\u7684<\/td>\n<td>\u9ad8\u7684<\/td>\n<td>\u9009\u4fee\u7684<\/td>\n<td>\u662f\u7684<\/td>\n<td>\u7ebf\u6027<\/td>\n<\/tr>\n<tr>\n<td>\u4e3b\u6210\u5206\u5206\u6790\uff08PCA\uff09<\/td>\n<td>\u4e0d<\/td>\n<td>\u4f4e\u7684<\/td>\n<td>\u4e0d<\/td>\n<td>\u4e0d<\/td>\n<td>\u7ebf\u6027<\/td>\n<\/tr>\n<tr>\n<td>\u72ec\u7acb\u6210\u5206\u5206\u6790\uff08ICA\uff09<\/td>\n<td>\u4e0d<\/td>\n<td>\u4f4e\u7684<\/td>\n<td>\u9009\u4fee\u7684<\/td>\n<td>\u4e0d<\/td>\n<td>\u7ebf\u6027<\/td>\n<\/tr>\n<tr>\n<td>\u6f5c\u5728\u72c4\u5229\u514b\u96f7\u5206\u914d (LDA)<\/td>\n<td>\u4e0d<\/td>\n<td>\u9ad8\u7684<\/td>\n<td>\u758f<\/td>\n<td>\u4e0d<\/td>\n<td>\u7ebf\u6027<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li>\n<p><strong>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff08NMF\uff09\uff1a<\/strong> NMF \u5bf9\u57fa\u548c\u7cfb\u6570\u77e9\u9635\u5f3a\u5236\u975e\u8d1f\u7ea6\u675f\uff0c\u4ece\u800c\u4ea7\u751f\u57fa\u4e8e\u90e8\u5206\u7684\u53ef\u89e3\u91ca\u6570\u636e\u8868\u793a\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u4e3b\u6210\u5206\u5206\u6790\uff08PCA\uff09\uff1a<\/strong> PCA \u662f\u4e00\u79cd\u7ebf\u6027\u6280\u672f\uff0c\u53ef\u6700\u5927\u5316\u65b9\u5dee\u5e76\u63d0\u4f9b\u6b63\u4ea4\u5206\u91cf\uff0c\u4f46\u5b83\u4e0d\u80fd\u4fdd\u8bc1\u53ef\u89e3\u91ca\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u72ec\u7acb\u6210\u5206\u5206\u6790\uff08ICA\uff09\uff1a<\/strong> ICA \u65e8\u5728\u5bfb\u627e\u7edf\u8ba1\u4e0a\u72ec\u7acb\u7684\u6210\u5206\uff0c\u5b83\u6bd4 PCA \u66f4\u6613\u4e8e\u89e3\u91ca\uff0c\u4f46\u4e0d\u80fd\u4fdd\u8bc1\u7a00\u758f\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6f5c\u5728\u72c4\u5229\u514b\u96f7\u5206\u914d\uff08LDA\uff09\uff1a<\/strong> LDA \u662f\u4e00\u79cd\u7528\u4e8e\u6587\u672c\u6570\u636e\u4e3b\u9898\u5efa\u6a21\u7684\u6982\u7387\u6a21\u578b\u3002\u5b83\u63d0\u4f9b\u7a00\u758f\u8868\u793a\uff0c\u4f46\u7f3a\u4e4f\u975e\u8d1f\u6027\u7ea6\u675f\u3002<\/p>\n<\/li>\n<\/ul>\n<h2>\u4e0e\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff08NMF\uff09\u76f8\u5173\u7684\u672a\u6765\u89c2\u70b9\u548c\u6280\u672f\u3002<\/h2>\n<p>\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u4ecd\u7136\u662f\u7814\u7a76\u548c\u5f00\u53d1\u7684\u6d3b\u8dc3\u9886\u57df\u3002\u4e0e NMF \u76f8\u5173\u7684\u4e00\u4e9b\u89c2\u70b9\u548c\u672a\u6765\u6280\u672f\u5982\u4e0b\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u6df1\u5ea6\u5b66\u4e60\u96c6\u6210\uff1a<\/strong> \u5c06 NMF \u4e0e\u6df1\u5ea6\u5b66\u4e60\u67b6\u6784\u76f8\u7ed3\u5408\u53ef\u4ee5\u589e\u5f3a\u6df1\u5ea6\u6a21\u578b\u7684\u7279\u5f81\u63d0\u53d6\u548c\u53ef\u89e3\u91ca\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7a33\u5065\u4e14\u53ef\u6269\u5c55\u7684\u7b97\u6cd5\uff1a<\/strong> \u6b63\u5728\u8fdb\u884c\u7684\u7814\u7a76\u91cd\u70b9\u662f\u5f00\u53d1\u5f3a\u5927\u4e14\u53ef\u6269\u5c55\u7684 NMF \u7b97\u6cd5\uff0c\u4ee5\u6709\u6548\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u96c6\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7279\u5b9a\u9886\u57df\u7684\u5e94\u7528\u7a0b\u5e8f\uff1a<\/strong> \u9488\u5bf9\u7279\u5b9a\u9886\u57df\uff08\u4f8b\u5982\u533b\u5b66\u6210\u50cf\u3001\u6c14\u5019\u5efa\u6a21\u548c\u793e\u4ea4\u7f51\u7edc\uff09\u5b9a\u5236 NMF \u7b97\u6cd5\u53ef\u4ee5\u5f00\u542f\u65b0\u7684\u89c1\u89e3\u548c\u5e94\u7528\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u786c\u4ef6\u52a0\u901f\uff1a<\/strong> \u968f\u7740\u4e13\u7528\u786c\u4ef6\uff08\u4f8b\u5982 GPU \u548c TPU\uff09\u7684\u8fdb\u6b65\uff0cNMF \u8ba1\u7b97\u53ef\u4ee5\u663e\u8457\u52a0\u901f\uff0c\u4ece\u800c\u5b9e\u73b0\u5b9e\u65f6\u5e94\u7528\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5728\u7ebf\u548c\u589e\u91cf\u5b66\u4e60\uff1a<\/strong> \u5728\u7ebf\u548c\u589e\u91cf NMF \u7b97\u6cd5\u7684\u7814\u7a76\u53ef\u4ee5\u5b9e\u73b0\u5bf9\u52a8\u6001\u6570\u636e\u6d41\u7684\u6301\u7eed\u5b66\u4e60\u548c\u9002\u5e94\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u4ee3\u7406\u670d\u52a1\u5668\u5982\u4f55\u4f7f\u7528\u6216\u4e0e\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff08NMF\uff09\u5173\u8054\u3002<\/h2>\n<p>\u4ee3\u7406\u670d\u52a1\u5668\u5728\u4e92\u8054\u7f51\u901a\u4fe1\u4e2d\u8d77\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u5145\u5f53\u5ba2\u6237\u7aef\u548c\u670d\u52a1\u5668\u4e4b\u95f4\u7684\u4e2d\u4ecb\u3002\u5c3d\u7ba1 NMF \u4e0e\u4ee3\u7406\u670d\u52a1\u5668\u6ca1\u6709\u76f4\u63a5\u5173\u8054\uff0c\u4f46\u5b83\u53ef\u4ee5\u4ece\u4ee5\u4e0b\u7528\u4f8b\u4e2d\u95f4\u63a5\u53d7\u76ca\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u7f51\u7edc\u7f13\u5b58\uff1a<\/strong> \u4ee3\u7406\u670d\u52a1\u5668\u4f7f\u7528 Web \u7f13\u5b58\u5c06\u7ecf\u5e38\u8bbf\u95ee\u7684\u5185\u5bb9\u5b58\u50a8\u5728\u672c\u5730\u3002\u53ef\u4ee5\u4f7f\u7528 NMF \u6765\u8bc6\u522b\u6700\u76f8\u5173\u4e14\u4fe1\u606f\u91cf\u6700\u5927\u7684\u5185\u5bb9\u8fdb\u884c\u7f13\u5b58\uff0c\u4ece\u800c\u63d0\u9ad8\u7f13\u5b58\u673a\u5236\u7684\u6548\u7387\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7528\u6237\u884c\u4e3a\u5206\u6790\uff1a<\/strong> \u4ee3\u7406\u670d\u52a1\u5668\u53ef\u4ee5\u6355\u83b7\u7528\u6237\u884c\u4e3a\u6570\u636e\uff0c\u4f8b\u5982 Web \u8bf7\u6c42\u548c\u6d4f\u89c8\u6a21\u5f0f\u3002\u7136\u540e\u53ef\u4ee5\u4f7f\u7528 NMF \u4ece\u8fd9\u4e9b\u6570\u636e\u4e2d\u63d0\u53d6\u6f5c\u5728\u7279\u5f81\uff0c\u5e2e\u52a9\u8fdb\u884c\u7528\u6237\u5206\u6790\u548c\u6709\u9488\u5bf9\u6027\u7684\u5185\u5bb9\u4ea4\u4ed8\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5f02\u5e38\u68c0\u6d4b\uff1a<\/strong> NMF \u53ef\u7528\u4e8e\u5206\u6790\u901a\u8fc7\u4ee3\u7406\u670d\u52a1\u5668\u7684\u6d41\u91cf\u6a21\u5f0f\u3002\u901a\u8fc7\u8bc6\u522b\u5f02\u5e38\u6a21\u5f0f\uff0c\u4ee3\u7406\u670d\u52a1\u5668\u53ef\u4ee5\u68c0\u6d4b\u7f51\u7edc\u6d3b\u52a8\u4e2d\u7684\u6f5c\u5728\u5b89\u5168\u5a01\u80c1\u548c\u5f02\u5e38\u60c5\u51b5\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5185\u5bb9\u8fc7\u6ee4\u548c\u5206\u7c7b\uff1a<\/strong> NMF \u53ef\u4ee5\u534f\u52a9\u4ee3\u7406\u670d\u52a1\u5668\u8fdb\u884c\u5185\u5bb9\u8fc7\u6ee4\u548c\u5206\u7c7b\uff0c\u5e2e\u52a9\u6839\u636e\u5185\u5bb9\u7684\u7279\u5f81\u548c\u6a21\u5f0f\u963b\u6b62\u6216\u5141\u8bb8\u7279\u5b9a\u7c7b\u578b\u7684\u5185\u5bb9\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u76f8\u5173\u94fe\u63a5<\/h2>\n<p>\u6709\u5173\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff08NMF\uff09\u7684\u66f4\u591a\u4fe1\u606f\uff0c\u8bf7\u53c2\u8003\u4ee5\u4e0b\u8d44\u6e90\uff1a<\/p>\n<ol>\n<li>\n<p><a href=\"https:\/\/www.nature.com\/articles\/44565\" target=\"_new\" rel=\"noopener nofollow\">\u901a\u8fc7\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u5b66\u4e60\u7269\u4f53\u7684\u5404\u4e2a\u90e8\u5206 - Daniel D. Lee \u548c H. Sebastian Seung<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Non-negative_matrix_factorization\" target=\"_new\" rel=\"noopener nofollow\">\u975e\u8d1f\u77e9\u9635\u5206\u89e3 - \u7ef4\u57fa\u767e\u79d1<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/www.datacamp.com\/community\/tutorials\/tutorial-nmf-python\" target=\"_new\" rel=\"noopener nofollow\">\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u7b80\u4ecb\uff1a\u7efc\u5408\u6307\u5357 - Datacamp<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/towardsdatascience.com\/nmf-unsupervised-feature-extraction-e1582b4e5afe\" target=\"_new\" rel=\"noopener nofollow\">\u975e\u8d1f\u77e9\u9635\u5206\u89e3\uff1a\u7406\u89e3\u6570\u5b66\u53ca\u5176\u5de5\u4f5c\u539f\u7406 \u2013 Medium<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/arxiv.org\/abs\/2002.01460\" target=\"_new\" rel=\"noopener nofollow\">\u4f7f\u7528\u975e\u8d1f\u77e9\u9635\u5206\u89e3\u8fdb\u884c\u56fe\u50cf\u7f16\u7801\u7684\u6df1\u5ea6\u5b66\u4e60 - arXiv<\/a><\/p>\n<\/li>\n<\/ol>","protected":false},"featured_media":469015,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-478216","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Non-negative Matrix Factorization (NMF)<\/mark>","faq_items":[{"question":"What is Non-negative Matrix Factorization (NMF)?","answer":"<p>Non-negative Matrix Factorization (NMF) is a powerful mathematical technique used for data analysis, feature extraction, and dimensionality reduction. It decomposes a non-negative data matrix into two or more non-negative matrices, providing interpretable results with additive components.<\/p>"},{"question":"How does Non-negative Matrix Factorization (NMF) work?","answer":"<p>NMF approximates a non-negative data matrix (V) by finding two non-negative matrices (W and H) such that V \u2248 WH. The basis matrix (W) represents meaningful features, and the coefficient matrix (H) indicates their relevance in each data sample.<\/p>"},{"question":"What are the key features of Non-negative Matrix Factorization (NMF)?","answer":"<p>The key features of NMF include the non-negativity constraint, parts-based representation, dimensionality reduction, interpretability, robustness to missing data, and flexibility in optimization techniques.<\/p>"},{"question":"What types of Non-negative Matrix Factorization (NMF) exist?","answer":"<p>There are various types of NMF, such as classic NMF, sparse NMF, robust NMF, hierarchical NMF, kernel NMF, and supervised NMF, each tailored for specific applications and constraints.<\/p>"},{"question":"How can Non-negative Matrix Factorization (NMF) be used?","answer":"<p>NMF finds applications in image processing, text mining, bioinformatics, audio signal processing, recommendation systems, and more. It aids in tasks like image compression, topic modeling, gene expression analysis, and source separation.<\/p>"},{"question":"What are the challenges and solutions related to Non-negative Matrix Factorization (NMF)?","answer":"<p>Challenges in NMF include initialization sensitivity, divergence issues, overfitting, data scaling, and handling missing data. These can be addressed by using appropriate initialization strategies, update rules, regularization, and imputation techniques.<\/p>"},{"question":"How does Non-negative Matrix Factorization (NMF) compare to other techniques?","answer":"<p>NMF stands out with its non-negativity constraint, interpretability, and sparsity control. In comparison, techniques like PCA, ICA, and LDA may offer orthogonal components, independence, or topic modeling but lack certain features of NMF.<\/p>"},{"question":"What are the future perspectives of Non-negative Matrix Factorization (NMF)?","answer":"<p>The future of NMF includes integrations with deep learning, development of robust and scalable algorithms, domain-specific applications, hardware acceleration, and advancements in online and incremental learning techniques.<\/p>"},{"question":"How can proxy servers be associated with Non-negative Matrix Factorization (NMF)?","answer":"<p>While not directly linked, proxy servers can benefit from NMF in web caching, user behavior analysis, anomaly detection, content filtering, and classification, leading to more efficient and secure internet communication.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/478216","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/478216\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media\/469015"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media?parent=478216"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}