{"id":815,"date":"2024-10-06T12:47:53","date_gmt":"2024-10-06T12:47:53","guid":{"rendered":"https:\/\/blue16.cn\/?p=815"},"modified":"2024-10-26T07:22:58","modified_gmt":"2024-10-26T07:22:58","slug":"%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e7%9b%b8%e5%85%b3%e6%95%b0%e5%ad%a6%e7%9f%a5%e8%af%86","status":"publish","type":"post","link":"https:\/\/blue16.cn\/index.php\/2024\/10\/06\/815\/","title":{"rendered":"\u673a\u5668\u5b66\u4e60\u76f8\u5173\u6570\u5b66\u77e5\u8bc6"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u524d\u8a00<\/h2>\n\n\n\n<p>\u673a\u5668\u5b66\u4e60\uff0c\u53c8\u53eb<strong>\u7edf\u8ba1\u5b66\u4e60<\/strong>\u3002\u65e2\u7136\u662f\u548c\u6570\u5b66\u76f8\u5173\u7684\uff0c\u80af\u5b9a\u8981\u5b66\u4e60\u76f8\u5173\u7684\u6570\u5b66\u77e5\u8bc6\uff0c\u624d\u80fd\u66f4\u597d\u5730\u7406\u89e3\u5404\u79cd\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u3002\u8fd9\u7bc7\u6587\u7ae0\u8bb0\u5f55\u4e86\u6211\u5728\u5b66\u4e60\u673a\u5668\u5b66\u4e60\u4e2d\u9047\u5230\u7684\u90e8\u5206\u6570\u5b66\u77e5\u8bc6\u4ee5\u53ca\u6211\u5bf9\u4ed6\u4eec\u7684\u7406\u89e3\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7ebf\u6027\u4ee3\u6570<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5411\u91cf\u3001\u77e9\u9635\u3001\u5f20\u91cf<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u5411\u91cf\uff08Vector\uff09<\/h4>\n\n\n\n<p><strong>\u4e00\u7ef4\u6570\u7ec4<\/strong>\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u77e9\u9635\u7684<strong>\u4e00\u7ef4\u5f62\u5f0f<\/strong>\uff0c\u901a\u5e38\u7528\u6765\u8868\u793a\u7a7a\u95f4\u4e2d\u7684\u70b9\u6216\u65b9\u5411\u3002\u4f8b\u5982\uff0c\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u70b9\u53ef\u4ee5\u8868\u793a\u4e3a\u4e00\u4e2a\u4e09\u7ef4\u5411\u91cf\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u77e9\u9635\uff08Matrix\uff09<\/h4>\n\n\n\n<p><strong>\u4e8c\u7ef4\u6570\u7ec4<\/strong>\uff0c\u901a\u5e38\u7528\u6765\u8868\u793a\u7ebf\u6027\u53d8\u6362\u3002\u4f8b\u5982\uff0c\u4e00\u4e2a2&#215;2\u7684\u77e9\u9635\u53ef\u4ee5\u8868\u793a\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u7684\u65cb\u8f6c\u6216\u7f29\u653e\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u5f20\u91cf\uff08Tensor\uff09<\/h4>\n\n\n\n<p><strong>\u591a\u7ef4\u6570\u7ec4<\/strong>\uff0c\u53ef\u4ee5\u8868\u793a\u6bd4\u77e9\u9635\u66f4\u9ad8\u7ef4\u7684\u6570\u636e\u7ed3\u6784\u3002\u4f8b\u5982\uff0c\u4e00\u4e2a\u4e09\u7ef4\u5f20\u91cf\u53ef\u4ee5\u7528\u6765\u8868\u793a\u4e00\u4e2a\u5f69\u8272\u56fe\u50cf\uff0c\u5176\u4e2d\u6bcf\u4e2a\u7ef4\u5ea6\u5206\u522b\u5bf9\u5e94\u9ad8\u5ea6\u3001\u5bbd\u5ea6\u548c\u989c\u8272\u901a\u9053\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u7684\u4e58\u6cd5\u8fd0\u7b97\u6027\u8d28<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(AB)C=A(BC)<\/li>\n\n\n\n<li>A(B+C)=AB+AC<\/li>\n\n\n\n<li>AB!=BA<\/li>\n\n\n\n<li>IA=A AI=A<\/li>\n\n\n\n<li>A0=0 0A=0<\/li>\n\n\n\n<li>\u5982\u679c A\u662f\u4e00\u4e2a m\u00d7n \u7684\u77e9\u9635\uff0cB \u662f\u4e00\u4e2a n\u00d7p \u7684\u77e9\u9635\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u4e58\u79ef C=AB \u5c06\u662f\u4e00\u4e2am\u00d7p \u7684\u77e9\u9635\u3002\u8fd9\u610f\u5473\u7740\u7b2c\u4e00\u4e2a\u77e9\u9635\u7684\u5217\u6570\u5fc5\u987b\u7b49\u4e8e\u7b2c\u4e8c\u4e2a\u77e9\u9635\u7684\u884c\u6570\u3002<\/li>\n\n\n\n<li>c(AB)=(cA)B=A(cB)\u8fd9\u8bf4\u660e\u6807\u91cf\u53ef\u4ee5\u5206\u914d\u5230\u77e9\u9635\u4e58\u6cd5\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u56e0\u5b50\u4e0a\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u7684\u5e42\u8fd0\u7b97<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u77e9\u9635\u7684\u5206\u6570\u5e42<\/h4>\n\n\n\n<p>A<sup>1\/2<\/sup>=B\u76f8\u5f53\u4e8e\u627e\u5230\u4e00\u4e2aB<sup>2<\/sup>\u4f7f\u5f97B<sup>2<\/sup>=A<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u964d\u4f4e\u77e9\u9635\u7684\u79e9<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e3a\u4ec0\u4e48\u8981\u964d\u4f4e\uff1f<\/h4>\n\n\n\n<p><strong>\u81ea\u7531\u5ea6<\/strong>\uff1a\u53ef\u4ee5\u7406\u89e3\u4e3a\u77e9\u9635\u4e2d\u80fd\u591f\u72ec\u7acb\u53d8\u5316\u7684\u5143\u7d20\u7684\u6570\u91cf\u3002<\/p>\n\n\n\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u964d\u4f4e\u77e9\u9635\u7684\u79e9\u901a\u5e38\u7528\u4e8e\u6570\u636e\u538b\u7f29\u3001\u7279\u5f81\u9009\u62e9\u3001\u4fe1\u53f7\u5904\u7406\u7b49\u9886\u57df\uff0c\u901a\u8fc7\u53bb\u9664\u5197\u4f59\u4fe1\u606f\u6765\u7b80\u5316\u95ee\u9898\u6216\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u89c1\u8fc7\u7684\u964d\u4f4e\u65b9\u6cd5<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\">\u77e9\u9635\u4e58\u6cd5<\/h5>\n\n\n\n<p>\u5c06\u77e9\u9635\u4e0e\u53e6\u4e00\u4e2a\u77e9\u9635\u76f8\u4e58\uff0c\u5982\u679c\u7b2c\u4e8c\u4e2a\u77e9\u9635\u7684\u79e9\u5c0f\u4e8e\u539f\u59cb\u77e9\u9635\u7684\u79e9\uff0c\u90a3\u4e48\u4e58\u79ef\u77e9\u9635\u7684\u79e9\u4e5f\u4f1a\u964d\u4f4e\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u8f6c\u7f6e\u7684\u8fd0\u7b97\u89c4\u5219<\/h3>\n\n\n\n<p>\u77e9\u9635\u8f6c\u7f6e\u6709\u4e00\u4e9b\u57fa\u672c\u7684\u6027\u8d28\uff0c\u6bd4\u5982\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>( (A^T)^T = A )\uff0c\u5373\u8f6c\u7f6e\u4e24\u6b21\u77e9\u9635\u4f1a\u56de\u5230\u539f\u77e9\u9635\u3002<\/li>\n\n\n\n<li>( (A + B)^T = A^T + B^T )\uff0c\u5373\u4e24\u4e2a\u77e9\u9635\u76f8\u52a0\u540e\u8f6c\u7f6e\u7b49\u4e8e\u8fd9\u4e24\u4e2a\u77e9\u9635\u5206\u522b\u8f6c\u7f6e\u540e\u518d\u76f8\u52a0\u3002<\/li>\n\n\n\n<li>( (KA)^T = K(A^T) )\uff0c\u5176\u4e2d( K )\u662f\u4e00\u4e2a\u5e38\u6570\uff0c\u8868\u660e\u77e9\u9635\u4e58\u4ee5\u5e38\u6570\u540e\u8f6c\u7f6e\u7b49\u4e8e\u8fd9\u4e2a\u5e38\u6570\u4e58\u4ee5\u77e9\u9635\u8f6c\u7f6e\u3002<\/li>\n\n\n\n<li>( (AB)^T = B^T A^T )\uff0c\u5373\u4e24\u4e2a\u77e9\u9635\u76f8\u4e58\u540e\u7684\u8f6c\u7f6e\u7b49\u4e8e\u7b2c\u4e8c\u4e2a\u77e9\u9635\u7684\u8f6c\u7f6e\u4e58\u4ee5\u7b2c\u4e00\u4e2a\u77e9\u9635\u7684\u8f6c\u7f6e\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u53ef\u9006<\/h3>\n\n\n\n<p>\u77e9\u9635\u53ef\u9006\u662f\u6307\u4e00\u4e2a\u65b9\u9635\uff08\u5373\u884c\u6570\u548c\u5217\u6570\u76f8\u7b49\u7684\u77e9\u9635\uff09\u5b58\u5728\u4e00\u4e2a\u9006\u77e9\u9635\uff0c\u4f7f\u5f97\u8fd9\u4e24\u4e2a\u77e9\u9635\u76f8\u4e58\u7684\u7ed3\u679c\u662f\u5355\u4f4d\u77e9\u9635\u3002<strong>\u5355\u4f4d\u77e9\u9635\u662f\u4e00\u4e2a\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u90fd\u662f1\uff0c\u800c\u5176\u4ed6\u4f4d\u7f6e\u4e0a\u7684\u5143\u7d20\u90fd\u662f0\u7684\u65b9\u9635<\/strong>\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u6765\u8bf4\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684n\u00d7n\u65b9\u9635A\uff0c\u5982\u679c\u5b58\u5728\u53e6\u4e00\u4e2an\u00d7n\u65b9\u9635B\uff0c\u4f7f\u5f97\u4ee5\u4e0b\u7b49\u5f0f\u6210\u7acb\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-27.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"398\" height=\"114\" data-original=\"https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-27.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-974\" style=\"width:168px;height:auto\"  sizes=\"auto, (max-width: 398px) 100vw, 398px\" \/><\/div><\/figure>\n<\/div>\n\n\n<p>\u5176\u4e2dI<em>I<\/em>\u662fn\u00d7n\u7684\u5355\u4f4d\u77e9\u9635\uff0c\u90a3\u4e48\u6211\u4eec\u79f0\u77e9\u9635A\u662f\u53ef\u9006\u7684\uff0c\u5e76\u4e14\u77e9\u9635B\u88ab\u79f0\u4e3aA\u7684\u9006\u77e9\u9635\uff0c\u901a\u5e38\u8bb0\u4f5cA<sup>-1<\/sup>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u7684\u8ff9<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u5b9a\u4e49<\/h4>\n\n\n\n<p>\u8ff9\u662f\u6307\u4e00\u4e2a\u65b9\u9635\uff08\u884c\u6570\u4e0e\u5217\u6570\u76f8\u7b49\u7684\u77e9\u9635\uff09\u7684<strong>\u4e3b\u5bf9\u89d2\u7ebf<\/strong>\uff08\u4ece\u5de6\u4e0a\u5230\u53f3\u4e0b\u7684\u7ebf\uff09\u4e0a<strong>\u6240\u6709\u5143\u7d20\u7684\u548c<\/strong>\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u8ff9\u5c31\u662f<strong>\u6cbf\u7740\u4e3b\u5bf9\u89d2\u7ebf\u4ece\u5de6\u4e0a\u89d2\u5230\u53f3\u4e0b\u89d2\u7684\u6240\u6709\u5143\u7d20\u7684\u7d2f\u52a0\u548c<\/strong>\u3002<\/p>\n\n\n\n<p>\u8ff9\u8fd0\u7b97\u53ea\u5b9a\u4e49\u5728<strong>\u65b9\u9635<\/strong>\u4e0a\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u8fd0\u7b97\u6027\u8d28<\/h4>\n\n\n\n<p><strong>1.\u7ebf\u6027<\/strong>\uff1a\u5bf9\u4e8e\u4efb\u610f\u4e24\u4e2a\u00a0n\u00d7n\u00a0\u77e9\u9635\u00a0A\u00a0\u548c\u00a0B\uff0c\u4ee5\u53ca\u4efb\u610f\u6807\u91cf\u00a0c\uff0c\u6709<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-55.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"846\" height=\"358\" data-original=\"https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-55.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1124\" style=\"width:196px;height:auto\"  sizes=\"auto, (max-width: 846px) 100vw, 846px\" \/><\/div><\/figure>\n<\/div>\n\n\n<p><strong>2.\u5faa\u73af\u4e0d\u53d8\u6027<\/strong>\uff1a\u5bf9\u4e8e\u4efb\u610fn\u00d7n\u77e9\u9635A\u548cB\uff0c\u6709<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-56.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"142\" data-original=\"https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-56.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1125\" style=\"width:220px;height:auto\"  sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><\/div><\/figure>\n<\/div>\n\n\n<p>\u5373\u4f7f\u00a0A<em>A<\/em>\u00a0\u548c\u00a0B<em>B<\/em>\u00a0\u4e0d\u4e00\u5b9a\u662f\u65b9\u9635\uff0c\u53ea\u8981\u5b83\u4eec\u7684\u4e58\u79efAB\u548cBA\u6709\u610f\u4e49\uff0c\u4e0a\u8ff0\u6027\u8d28\u4e5f\u6210\u7acb\u3002<\/p>\n\n\n\n<p><strong>3.\u5bf9\u6362\u6027<\/strong>\uff1a\u5bf9\u4e8e\u4efb\u610f\u00a0n\u00d7n\u77e9\u9635\u00a0A\uff0c\u6709<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-57.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"438\" height=\"132\" data-original=\"https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-57.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1126\" style=\"width:153px;height:auto\"  sizes=\"auto, (max-width: 438px) 100vw, 438px\" \/><\/div><\/figure>\n<\/div>\n\n\n<p><strong>4.\u8ff9\u7684\u5faa\u73af\u6027\u8d28<\/strong>\uff08Cycle Property of Trace\uff09\uff1a\u5bf9\u4e8e\u4efb\u610f\u7684\u77e9\u9635 A\u3001B \u548c C\uff0c\u6709\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center\">tr(<em>ABC<\/em>)=tr(<em>BCA<\/em>)=tr(<em>CAB<\/em>)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u5947\u5f02\/\u4e0d\u5947\u5f02<\/h3>\n\n\n\n<p>\u7b49\u4ef7\u4e8e\u8bf4<strong>\u77e9\u9635\u662f\u5426\u53ef\u9006<\/strong>\uff0c\u77e9\u9635\u5947\u5f02\u610f\u5473\u7740\u77e9\u9635\u4e0d\u53ef\u9006\uff0c\u77e9\u9635\u4e0d\u5947\u5f02\u610f\u5473\u7740\u77e9\u9635\u53ef\u9006\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5947\u5f02\u503c\u5206\u89e3\uff08singular value decomposition,SVD\uff09<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u5b9a\u4e49<\/h4>\n\n\n\n<p>\u5947\u5f02\u503c\u5206\u89e3\uff08SVD, Singular Value Decomposition\uff09\u662f\u4e00\u79cd\u5728\u77e9\u9635\u7406\u8bba\u4e2d\u975e\u5e38\u91cd\u8981\u7684\u7ebf\u6027\u4ee3\u6570\u5de5\u5177\uff0c\u5b83\u53ef\u4ee5\u5c06\u4efb\u610f\u4e00\u4e2am\u00d7n<em>m<\/em>\u00d7<em>n<\/em>\u7684\u77e9\u9635A<em>A<\/em>\u5206\u89e3\u4e3a\u4e09\u4e2a\u77e9\u9635\u7684\u4e58\u79ef\u5f62\u5f0f\uff0c\u5373\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"160\" height=\"74\" data-original=\"https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-817\" style=\"width:123px;height:auto\"\/><\/div><\/figure>\n<\/div>\n\n\n<p>\u8fd9\u91cc\u7684\u4e09\u4e2a\u77e9\u9635\u5177\u6709\u4ee5\u4e0b\u7279\u6027\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>U\u662f\u4e00\u4e2am\u00d7m\u7684\u5355\u4f4d\u6b63\u4ea4\u77e9\u9635\uff0c\u5b83\u7684\u5217\u5411\u91cf\u79f0\u4e3a\u5de6\u5947\u5f02\u5411\u91cf\uff0c\u5b83\u4eec\u6784\u6210\u4e86\u77e9\u9635A\u884c\u7a7a\u95f4\u7684\u4e00\u4e2a\u6b63\u4ea4\u57fa\u3002<\/li>\n\n\n\n<li>\u03a3\u662f\u4e00\u4e2am\u00d7n\u7684\u5bf9\u89d2\u77e9\u9635\uff0c\u4f46\u9664\u4e86\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u5916\uff0c\u5176\u4ed6\u4f4d\u7f6e\u90fd\u662f0\u3002<strong>\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u975e\u8d1f\u6570\u79f0\u4e3a\u5947\u5f02\u503c<\/strong>\uff0c\u5b83\u4eec\u6309\u7167\u4ece\u5927\u5230\u5c0f\u7684\u987a\u5e8f\u6392\u5217\uff0c<strong>\u5947\u5f02\u503c\u7684\u6570\u76ee\u7b49\u4e8eA\u7684\u79e9<\/strong>\u3002\u5947\u5f02\u503c\u7684\u5927\u5c0f\u8868\u793a\u4e86\u539f\u77e9\u9635A\u5728\u5bf9\u5e94\u5947\u5f02\u5411\u91cf\u65b9\u5411\u4e0a\u7684\u201c\u62c9\u4f38\u201d\u7a0b\u5ea6\u3002<\/li>\n\n\n\n<li>VT\u662fn\u00d7n\u7684\u5355\u4f4d\u6b63\u4ea4\u77e9\u9635\u7684\u8f6c\u7f6e\uff0c\u5176\u884c\u5411\u91cf\u79f0\u4e3a\u53f3\u5947\u5f02\u5411\u91cf\uff0c\u5b83\u4eec\u6784\u6210\u4e86\u77e9\u9635A\u5217\u7a7a\u95f4\u7684\u4e00\u4e2a\u6b63\u4ea4\u57fa\u3002<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">\u4f5c\u7528<\/h4>\n\n\n\n<p>\u63ed\u793a\u77e9\u9635\u7684\u5185\u5728\u7ed3\u6784\uff0c\u901a\u8fc7\u5206\u89e3\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u77e9\u9635\u7684\u6027\u8d28\u548c\u884c\u4e3a\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5947\u5f02\u503c\u9608\u503c\u7b97\u5b50\uff08singular value thresholding\uff0cSVT\uff09<\/h3>\n\n\n\n<p>\u8fd8\u5728\u7814\u7a76&#8230;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u7684\u79e9<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u5b9a\u4e49<\/h4>\n\n\n\n<p>\u77e9\u9635\u7684\u79e9\u5c31\u662f\u77e9\u9635\u4e2d\u975e\u96f6\u5b50\u5f0f\u7684\u6700\u9ad8\u9636\u6570\u3002<\/p>\n\n\n\n<p>\u77e9\u9635\u7684\u79e9\u662f\u6307\u77e9\u9635\u4e2d\u7ebf\u6027\u65e0\u5173\u7684\u884c\uff08\u6216\u5217\uff09\u7684\u6700\u5927\u6570\u76ee\uff0c\u5b83\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u77e9\u9635\u7279\u5f81\uff0c\u53ef\u4ee5\u7528\u6765\u63cf\u8ff0\u77e9\u9635\u7684\u201c\u5927\u5c0f\u201d\u6216\u8005\u201c\u590d\u6742\u5ea6\u201d\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u77e9\u9635\u8303\u6570<\/h4>\n\n\n\n<p><strong>\u77e9\u9635\u8303\u6570<\/strong>\uff08matrix norm\uff09\u662f\u6570\u5b66\u4e0a\u5411\u91cf\u8303\u6570\u5bf9\u77e9\u9635\u7684\u4e00\u4e2a\u81ea\u7136\u63a8\u5e7f\u3002<\/p>\n\n\n\n<p><strong>\u8303\u6570<\/strong>(norm)\uff1a\u8303\u6570\u662f\u4e00\u79cd\u5728\u6570\u5b66\u548c\u7269\u7406\u5b66\u4e2d\u7528\u6765\u8861\u91cf\u5411\u91cf\u201c\u5927\u5c0f\u201d\u6216\u8005\u201c\u957f\u5ea6\u201d\u7684\u51fd\u6570\u3002\u66f4\u4e00\u822c\u5730\uff0c\u5b83\u53ef\u4ee5\u7528\u6765\u8861\u91cf\u51fd\u6570\u3001\u5e8f\u5217\u3001\u7b97\u5b50\u7b49\u6570\u5b66\u5bf9\u8c61\u7684\u201c\u5927\u5c0f\u201d\u3002\u5728\u4e0d\u540c\u7684\u6570\u5b66\u5206\u652f\u4e2d\uff0c\u8303\u6570\u7684\u5b9a\u4e49\u548c\u6027\u8d28\u53ef\u80fd\u6709\u6240\u4e0d\u540c\uff0c\u4f46\u5b83\u4eec\u90fd\u6709\u4e00\u4e9b\u5171\u540c\u7684\u57fa\u672c\u7279\u5f81\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u6b63\u5219\u5316<\/h4>\n\n\n\n<p>\u6b63\u5219\u5316\u662f\u4e00\u79cd\u5728\u673a\u5668\u5b66\u4e60\u548c\u7edf\u8ba1\u5b66\u4e60\u4e2d\u5bf9\u6a21\u578b\u8fdb\u884c\u4f18\u5316\u7684\u65b9\u6cd5\uff0c\u65e8\u5728\u9632\u6b62\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u8fc7\u5ea6\u62df\u5408\uff08overfitting\uff09\u3002\u8fc7\u5ea6\u62df\u5408\u662f\u6307\u6a21\u578b\u5bf9\u8bad\u7ec3\u6570\u636e\u5b66\u5f97\u201c\u592a\u597d\u201d\uff0c\u4ee5\u81f3\u4e8e\u5b83\u6355\u6349\u5230\u4e86\u6570\u636e\u4e2d\u7684\u566a\u58f0\u800c\u4e0d\u662f\u6f5c\u5728\u7684\u6a21\u5f0f\uff0c\u5bfc\u81f4\u6a21\u578b\u5728\u65b0\u7684\u3001\u672a\u89c1\u8fc7\u7684\u6570\u636e\u4e0a\u8868\u73b0\u4e0d\u4f73\u3002<br>\u6b63\u5219\u5316\u7684\u4e3b\u8981\u76ee\u7684\u662f\u901a\u8fc7\u4ee5\u4e0b\u51e0\u79cd\u65b9\u5f0f\u6765\u63d0\u9ad8\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u60e9\u7f5a\u590d\u6742\u6a21\u578b<\/strong>\uff1a\u901a\u8fc7\u7ed9\u6a21\u578b\u7684\u590d\u6742\u5ea6\u6dfb\u52a0\u60e9\u7f5a\u9879\uff0c\u9f13\u52b1\u6a21\u578b\u9009\u62e9\u53c2\u6570\u503c\u8f83\u5c0f\u7684\u89e3\uff0c\u4ece\u800c\u7b80\u5316\u6a21\u578b\u7ed3\u6784\u3002<\/li>\n\n\n\n<li><strong>\u63a7\u5236\u6a21\u578b\u6743\u91cd<\/strong>\uff1a\u6b63\u5219\u5316\u901a\u8fc7\u9650\u5236\u6743\u91cd\u7684\u5927\u5c0f\uff0c\u4f7f\u5f97\u6a21\u578b\u4e0d\u4f1a\u5bf9\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u968f\u673a\u566a\u58f0\u505a\u51fa\u5f3a\u70c8\u53cd\u5e94\u3002<br>\u5e38\u89c1\u7684\u6b63\u5219\u5316\u65b9\u6cd5\u5305\u62ec\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>L1\u6b63\u5219\u5316\uff08Lasso\u56de\u5f52\uff09<\/strong>\uff1a\u5728\u635f\u5931\u51fd\u6570\u4e2d\u6dfb\u52a0\u6743\u91cd\u7684\u7edd\u5bf9\u503c\u548c\u7684\u60e9\u7f5a\u9879\u3002\u8fd9\u53ef\u80fd\u5bfc\u81f4\u67d0\u4e9b\u6743\u91cd\u4e3a\u96f6\uff0c\u4ece\u800c\u5b9e\u73b0\u7279\u5f81\u7684\u81ea\u52a8\u9009\u62e9\u3002<\/li>\n\n\n\n<li><strong>L2\u6b63\u5219\u5316\uff08Ridge\u56de\u5f52\uff09<\/strong>\uff1a\u5728\u635f\u5931\u51fd\u6570\u4e2d\u6dfb\u52a0\u6743\u91cd\u7684\u5e73\u65b9\u548c\u7684\u60e9\u7f5a\u9879\u3002\u8fd9\u4f1a\u4f7f\u6743\u91cd\u5c3d\u91cf\u5c0f\uff0c\u4f46\u4e0d\u4f1a\u53d8\u6210\u96f6\u3002<\/li>\n\n\n\n<li><strong>\u5f39\u6027\u7f51\uff08Elastic Net\uff09<\/strong>\uff1a\u662fL1\u548cL2\u6b63\u5219\u5316\u7684\u7ec4\u5408\uff0c\u901a\u8fc7\u4e00\u4e2a\u53c2\u6570\u63a7\u5236\u4e24\u8005\u4e4b\u95f4\u7684\u5e73\u8861\u3002<\/li>\n\n\n\n<li><strong>Dropout<\/strong>\uff1a\u5728\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u65f6\uff0c\u968f\u673a\u5730\u201c\u4e22\u5f03\u201d\uff08\u5373\u8bbe\u7f6e\u8f93\u51fa\u4e3a\u96f6\uff09\u4e00\u4e9b\u795e\u7ecf\u5143\u53ca\u5176\u8fde\u63a5\uff0c\u4ee5\u51cf\u5c11\u6a21\u578b\u5bf9\u7279\u5b9a\u8bad\u7ec3\u6837\u672c\u7684\u4f9d\u8d56\u3002<\/li>\n\n\n\n<li><strong>\u6570\u636e\u589e\u5f3a<\/strong>\uff1a\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5bf9\u6570\u636e\u8fdb\u884c\u53d8\u6362\uff0c\u4eba\u4e3a\u5730\u6269\u5927\u8bad\u7ec3\u96c6\u7684\u89c4\u6a21\uff0c\u4ee5\u9632\u6b62\u6a21\u578b\u8bb0\u4f4f\u8bad\u7ec3\u6837\u672c\u3002<br>\u6b63\u5219\u5316\u662f\u63d0\u9ad8\u673a\u5668\u5b66\u4e60\u6a21\u578b\u6cdb\u5316\u80fd\u529b\u7684\u91cd\u8981\u6280\u672f\uff0c\u5b83\u5e2e\u52a9\u786e\u4fdd\u6a21\u578b\u80fd\u591f\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u66f4\u597d\u5730\u5de5\u4f5c\u3002\u5728\u8bbe\u8ba1\u6a21\u578b\u65f6\uff0c\u9009\u62e9\u5408\u9002\u7684\u6b63\u5219\u5316\u65b9\u6cd5\u5bf9\u4e8e\u83b7\u5f97\u4e00\u4e2a\u65e2\u7cbe\u786e\u53c8\u9c81\u68d2\u7684\u6a21\u578b\u81f3\u5173\u91cd\u8981\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u7684\u8ff9(trace)<\/h3>\n\n\n\n<p>\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\uff0ctr(A)\u8868\u793a\u77e9\u9635A\u7684\u8ff9\uff08trace\uff09\u3002\u8ff9\u662f\u4e00\u4e2a\u65b9\u9635\u7684\u6240\u6709\u5bf9\u89d2\u7ebf\u5143\u7d20\u4e4b\u548c\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5982\u679cA\u662f\u4e00\u4e2an\u00d7n\u7684\u77e9\u9635\uff0c\u90a3\u4e48\u5b83\u7684\u8ff9\u5c31\u662fA\u7684\u7b2c1\u884c\u7b2c1\u5217\u3001\u7b2c2\u884c\u7b2c2\u5217\u3001\u2026\u2026\u3001\u7b2cn\u884c\u7b2cn\u5217\u5143\u7d20\u7684\u548c\uff0c\u7528\u6570\u5b66\u516c\u5f0f\u8868\u793a\u5c31\u662f\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-19.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"406\" height=\"76\" data-original=\"https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-19.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-931\" style=\"width:230px;height:auto\"  sizes=\"auto, (max-width: 406px) 100vw, 406px\" \/><\/div><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\">\u6700\u4f18\u5316\u76f8\u5173<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u62c9\u683c\u6717\u65e5\u4e58\u6570\u6cd5<\/h3>\n\n\n\n<p>\u62c9\u683c\u6717\u65e5\u4e58\u6570\u6cd5\uff1a<\/p>\n\n\n\n<p><a href=\"https:\/\/blog.csdn.net\/Emma_Love\/article\/details\/85146800\">\u673a\u5668\u5b66\u4e60\u77e5\u8bc6\u70b9\u603b\u7ed3 &#8211; \u62c9\u683c\u6717\u65e5\u4e58\u5b50\u6cd5\uff08Lagrange Multiplier Method\uff09\u8be6\u89e3-CSDN\u535a\u5ba2<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u51f8\u4f18\u5316\u95ee\u9898\u7684\u5b9a\u4e49<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-12-1024x373.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"373\" data-original=\"https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-12-1024x373.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-920\" style=\"width:648px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-13-1024x51.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"51\" data-original=\"https:\/\/blue16.cn\/wp-content\/uploads\/2024\/10\/image-13-1024x51.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-922\" style=\"width:663px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\">\u51f8\u4e8c\u6b21\u89c4\u5212\u95ee\u9898 (QPP,Quadratic programming problem)<\/h3>\n\n\n\n<p>\u76ee\u6807\u51fd\u6570\u662f\u4e8c\u6b21\uff0c\u7ea6\u675f\u6761\u4ef6\u662f\u7ebf\u6027=&gt; \u51f8\u4e8c\u6b21\u89c4\u5212\u95ee\u9898 (QPP,Quadratic programming problem)\uff0c\u7406\u60f3\u60c5\u51b5\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e9bQP\u7684\u5957\u4ef6\u76f4\u63a5\u8fdb\u884c\u6c42\u89e3\u5f97\u5230\u7b54\u6848\uff0c\u4f46\u662f\u5b58\u5728\u6837\u672c\u7ef4\u5ea6\u8fc7\u9ad8\u6216\u8005\u6837\u672c\u6570\u5f88\u591a\uff0c\u6216\u8005\u5b58\u5728\u6837\u672c\u7279\u5f81\u5347\u7ef4\u7684\u4e00\u4e9b\u60c5\u51b5\uff0cQP\u53ef\u80fd\u5c31\u4e0d\u592a\u80fd\u591f\u76f4\u63a5\u6c42\u89e3\uff0c\u7531\u6b64\u5f15\u5165\u4e86\u5bf9\u5076\u6c42\u89e3\u7684\u6982\u5ff5\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">KKT\u6761\u4ef6<\/h3>\n\n\n\n<p>\u53c2\u8003\u6587\u7ae0\uff1a<a href=\"https:\/\/zhuanlan.zhihu.com\/p\/556931657\">KKT\u6761\u4ef6\uff0c\u539f\u6765\u5982\u6b64\u7b80\u5355 (\u4e0a) | \u7406\u8bba\u90e8\u5206 &#8211; \u77e5\u4e4e (zhihu.com)<\/a><\/p>\n\n\n\n<p><strong>\u200bKKT\u6761\u4ef6(Karush\u2013Kuhn\u2013Tucker conditions)<\/strong>\u662f\u6700\u4f18\u5316\uff08\u7279\u522b\u662f<strong>\u975e\u7ebf\u6027\u89c4\u5212<\/strong>\uff09\u9886\u57df\u6700\u91cd\u8981\u7684\u6210\u679c\u4e4b\u4e00\uff0c\u662f<strong>\u5224\u65ad\u67d0\u70b9\u662f\u6781\u503c\u70b9<\/strong>\u7684\u5fc5\u8981\u6761\u4ef6\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5bf9\u5076\u7406\u8bba<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Wolfe\u5bf9\u5076<\/h3>\n\n\n\n<p>dual form<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u524d\u8a00 \u673a\u5668\u5b66\u4e60\uff0c\u53c8\u53eb\u7edf\u8ba1\u5b66\u4e60\u3002\u65e2\u7136\u662f\u548c\u6570\u5b66\u76f8\u5173\u7684\uff0c\u80af\u5b9a\u8981\u5b66\u4e60\u76f8\u5173\u7684\u6570\u5b66\u77e5\u8bc6\uff0c\u624d\u80fd\u66f4\u597d\u5730\u7406\u89e3\u5404\u79cd\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u3002\u8fd9 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26,48,45],"tags":[],"class_list":["post-815","post","type-post","status-publish","format-standard","hentry","category-study","category-48","category-45"],"_links":{"self":[{"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/posts\/815","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/comments?post=815"}],"version-history":[{"count":13,"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/posts\/815\/revisions"}],"predecessor-version":[{"id":1133,"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/posts\/815\/revisions\/1133"}],"wp:attachment":[{"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/media?parent=815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/categories?post=815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blue16.cn\/index.php\/wp-json\/wp\/v2\/tags?post=815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}