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\u062a\u0643\u064a\u064a\u0641 NMF \u0645\u0639 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0645\u0645\u0627 \u064a\u0633\u0645\u062d \u0628\u0627\u0644\u062a\u062e\u0635\u064a\u0635 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u062e\u0635\u0627\u0626\u0635 \u0648\u0645\u062a\u0637\u0644\u0628\u0627\u062a \u0628\u064a\u0627\u0646\u0627\u062a \u0645\u062d\u062f\u062f\u0629.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0623\u0646\u0648\u0627\u0639 \u0639\u0648\u0627\u0645\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 (NMF)<\/h2>\n<p>\u0647\u0646\u0627\u0643 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u0627\u0644\u0625\u0636\u0627\u0641\u0627\u062a \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629\u060c \u0648\u0644\u0643\u0644 \u0645\u0646\u0647\u0627 \u0646\u0642\u0627\u0637 \u0627\u0644\u0642\u0648\u0629 \u0648\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0647\u0627. \u062a\u062a\u0636\u0645\u0646 \u0628\u0639\u0636 \u0627\u0644\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0634\u0627\u0626\u0639\u0629 \u0645\u0646 NMF \u0645\u0627 \u064a\u0644\u064a:<\/p>\n<ol>\n<li>\n<p><strong>\u0646\u0645\u0641 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629:<\/strong> \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629 \u0644\u0640 NMF \u0643\u0645\u0627 \u0627\u0642\u062a\u0631\u062d\u0647\u0627 Lee \u0648Seung\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0623\u0633\u0627\u0644\u064a\u0628 \u0645\u062b\u0644 \u0627\u0644\u062a\u062d\u062f\u064a\u062b\u0627\u062a \u0627\u0644\u0645\u0636\u0627\u0639\u0641\u0629 \u0623\u0648 \u062a\u0646\u0627\u0648\u0628 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0644\u0644\u062a\u062d\u0633\u064a\u0646.<\/p>\n<\/li>\n<li>\n<p><strong>NMF \u0645\u062a\u0641\u0631\u0642:<\/strong> \u064a\u0642\u062f\u0645 \u0647\u0630\u0627 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0642\u064a\u0648\u062f\u064b\u0627 \u0645\u062a\u0641\u0631\u0642\u0629\u060c \u0645\u0645\u0627 \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u062a\u0645\u062b\u064a\u0644 \u0623\u0643\u062b\u0631 \u0643\u0641\u0627\u0621\u0629 \u0648\u0642\u0627\u0628\u0644\u064a\u0629 \u0644\u0644\u062a\u0641\u0633\u064a\u0631 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/p>\n<\/li>\n<li>\n<p><strong>NMF \u0642\u0648\u064a:<\/strong> \u062a\u0645 \u062a\u0635\u0645\u064a\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a NMF \u0627\u0644\u0642\u0648\u064a\u0629 \u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u062a\u0637\u0631\u0641\u0629 \u0648\u0627\u0644\u0636\u0648\u0636\u0627\u0621 \u0641\u064a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0645\u0645\u0627 \u064a\u0648\u0641\u0631 \u0639\u0648\u0627\u0645\u0644 \u0623\u0643\u062b\u0631 \u0645\u0648\u062b\u0648\u0642\u064a\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>NMF \u0627\u0644\u0647\u0631\u0645\u064a:<\/strong> \u0641\u064a NMF \u0627\u0644\u0647\u0631\u0645\u064a\u060c \u064a\u062a\u0645 \u062a\u0646\u0641\u064a\u0630 \u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629 \u0645\u0646 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u060c \u0645\u0645\u0627 \u064a\u0633\u0645\u062d \u0628\u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0647\u0631\u0645\u064a \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/p>\n<\/li>\n<li>\n<p><strong>\u0646\u0648\u0627\u0629 NMF:<\/strong> \u064a\u0639\u0645\u0644 Kernel NMF \u0639\u0644\u0649 \u062a\u0648\u0633\u064a\u0639 \u0645\u0641\u0647\u0648\u0645 NMF \u0625\u0644\u0649 \u0645\u0633\u0627\u062d\u0629 \u0627\u0644\u0645\u064a\u0632\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0633\u0628\u0628\u0647\u0627 kernel\u060c \u0645\u0645\u0627 \u064a\u062a\u064a\u062d \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u063a\u064a\u0631 \u0627\u0644\u062e\u0637\u064a\u0629 \u0625\u0644\u0649 \u0639\u0648\u0627\u0645\u0644.<\/p>\n<\/li>\n<li>\n<p><strong>NMF \u0627\u0644\u062e\u0627\u0636\u0639\u0629 \u0644\u0644\u0625\u0634\u0631\u0627\u0641:<\/strong> \u064a\u062f\u0645\u062c \u0647\u0630\u0627 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u062a\u0633\u0645\u064a\u0627\u062a \u0627\u0644\u0641\u0626\u0629 \u0623\u0648 \u0627\u0644\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0647\u062f\u0641\u0629 \u0641\u064a \u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u060c \u0645\u0645\u0627 \u064a\u062c\u0639\u0644\u0647\u0627 \u0645\u0646\u0627\u0633\u0628\u0629 \u0644\u0645\u0647\u0627\u0645 \u0627\u0644\u062a\u0635\u0646\u064a\u0641.<\/p>\n<\/li>\n<\/ol>\n<p>\u064a\u0648\u062c\u062f \u0623\u062f\u0646\u0627\u0647 \u062c\u062f\u0648\u0644 \u064a\u0644\u062e\u0635 \u0627\u0644\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u0648\u062e\u0635\u0627\u0626\u0635\u0647\u0627:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0646\u0648\u0639 NMF<\/th>\n<th>\u0635\u0641\u0627\u062a<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0646\u0645\u0641 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629<\/td>\n<td>\u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629 \u0645\u0639 \u0642\u064a\u062f \u063a\u064a\u0631 \u0627\u0644\u0633\u0644\u0628\u064a\u0629<\/td>\n<\/tr>\n<tr>\n<td>NMF \u0645\u062a\u0641\u0631\u0642<\/td>\n<td>\u064a\u0642\u062f\u0645 \u0627\u0644\u062a\u0646\u0627\u062b\u0631 \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0646\u062a\u064a\u062c\u0629 \u0623\u0643\u062b\u0631 \u0642\u0627\u0628\u0644\u064a\u0629 \u0644\u0644\u062a\u0641\u0633\u064a\u0631<\/td>\n<\/tr>\n<tr>\n<td>NMF \u0642\u0648\u064a<\/td>\n<td>\u064a\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u062a\u0637\u0631\u0641\u0629 \u0648\u0627\u0644\u0636\u0648\u0636\u0627\u0621 \u0628\u0634\u0643\u0644 \u0641\u0639\u0627\u0644<\/td>\n<\/tr>\n<tr>\n<td>NMF \u0627\u0644\u0647\u0631\u0645\u064a<\/td>\n<td>\u064a\u0648\u0641\u0631 \u062a\u0645\u062b\u064a\u0644\u0627\u064b \u0647\u0631\u0645\u064a\u064b\u0627 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/td>\n<\/tr>\n<tr>\n<td>\u0646\u0648\u0627\u0629 \u0625\u0646 \u0625\u0645 \u0625\u0641<\/td>\n<td>\u064a\u0645\u062a\u062f NMF \u0625\u0644\u0649 \u0645\u0633\u0627\u062d\u0629 \u0627\u0644\u0645\u064a\u0632\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0633\u0628\u0628\u0647\u0627 kernel<\/td>\n<\/tr>\n<tr>\n<td>NMF \u0627\u0644\u062e\u0627\u0636\u0639\u0629 \u0644\u0644\u0625\u0634\u0631\u0627\u0641<\/td>\n<td>\u064a\u062a\u0636\u0645\u0646 \u062a\u0633\u0645\u064a\u0627\u062a \u0627\u0644\u0641\u0635\u0644 \u0644\u0645\u0647\u0627\u0645 \u0627\u0644\u062a\u0635\u0646\u064a\u0641<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0637\u0631\u0642 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0639\u0627\u0645\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 (NMF) \u0648\u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a \u0648\u062d\u0644\u0648\u0644\u0647\u0627 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645.<\/h2>\n<p>\u064a\u062d\u062a\u0648\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u0639\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0629 \u0648\u0627\u0633\u0639\u0629 \u0645\u0646 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0641\u064a \u0645\u062c\u0627\u0644\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629. \u0628\u0639\u0636 \u062d\u0627\u0644\u0627\u062a \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0634\u0627\u0626\u0639\u0629 \u0648\u0627\u0644\u062a\u062d\u062f\u064a\u0627\u062a \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0640 NMF \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<h3>\u062d\u0627\u0644\u0627\u062a \u0627\u0633\u062a\u062e\u062f\u0627\u0645 NMF:<\/h3>\n<ol>\n<li>\n<p><strong>\u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0635\u0648\u0631\u0629:<\/strong> \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 NMF \u0644\u0636\u063a\u0637 \u0627\u0644\u0635\u0648\u0631 \u0648\u062a\u0642\u0644\u064a\u0644 \u0627\u0644\u062a\u0634\u0648\u064a\u0634 \u0648\u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0627\u0644\u0645\u064a\u0632\u0627\u062a \u0641\u064a \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0635\u0648\u0631.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0646\u0635\u0648\u0635:<\/strong> \u064a\u0633\u0627\u0639\u062f NMF \u0641\u064a \u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0645\u0648\u0627\u0636\u064a\u0639 \u0648\u062a\u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0633\u062a\u0646\u062f\u0627\u062a \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0634\u0627\u0639\u0631 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0646\u0635\u064a\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u0645\u0639\u0644\u0648\u0645\u0627\u062a\u064a\u0629 \u0627\u0644\u062d\u064a\u0648\u064a\u0629:<\/strong> \u064a\u064f\u0633\u062a\u062e\u062f\u0645 NMF \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062c\u064a\u0646\u064a\u060c \u0648\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0623\u0646\u0645\u0627\u0637 \u0641\u064a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0628\u064a\u0648\u0644\u0648\u062c\u064a\u0629\u060c \u0648\u0627\u0643\u062a\u0634\u0627\u0641 \u0627\u0644\u0623\u062f\u0648\u064a\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0625\u0634\u0627\u0631\u0627\u062a \u0627\u0644\u0635\u0648\u062a\u064a\u0629:<\/strong> \u064a\u0633\u062a\u062e\u062f\u0645 NMF \u0644\u0641\u0635\u0644 \u0627\u0644\u0645\u0635\u062f\u0631 \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0648\u0633\u064a\u0642\u0649.<\/p>\n<\/li>\n<li>\n<p><strong>\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062a\u0648\u0635\u064a\u0629:<\/strong> \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 NMF \u0644\u0628\u0646\u0627\u0621 \u0623\u0646\u0638\u0645\u0629 \u062a\u0648\u0635\u064a\u0629 \u0645\u062e\u0635\u0635\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0639\u0648\u0627\u0645\u0644 \u0627\u0644\u0643\u0627\u0645\u0646\u0629 \u0641\u064a \u062a\u0641\u0627\u0639\u0644\u0627\u062a \u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645.<\/p>\n<\/li>\n<\/ol>\n<h3>\u0627\u0644\u062a\u062d\u062f\u064a\u0627\u062a \u0648\u0627\u0644\u062d\u0644\u0648\u0644:<\/h3>\n<ol>\n<li>\n<p><strong>\u0627\u0644\u062a\u0647\u064a\u0626\u0629:<\/strong> \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0643\u0648\u0646 NMF \u062d\u0633\u0627\u0633\u064b\u0627 \u0644\u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0644\u0640 W \u0648H. \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0633\u0627\u0639\u062f \u0627\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0627\u062a \u0627\u0644\u062a\u0647\u064a\u0626\u0629 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u062b\u0644 \u0627\u0644\u062a\u0647\u064a\u0626\u0629 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0623\u0648 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0642\u0646\u064a\u0627\u062a \u062a\u0642\u0644\u064a\u0644 \u0627\u0644\u0623\u0628\u0639\u0627\u062f \u0627\u0644\u0623\u062e\u0631\u0649 \u0641\u064a \u0645\u0639\u0627\u0644\u062c\u0629 \u0630\u0644\u0643.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u0634\u0639\u0628:<\/strong> \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0639\u0627\u0646\u064a \u0628\u0639\u0636 \u0623\u0633\u0627\u0644\u064a\u0628 \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0641\u064a NMF \u0645\u0646 \u0645\u0634\u0643\u0644\u0627\u062a \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u060c \u0645\u0645\u0627 \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u0628\u0637\u0621 \u0627\u0644\u062a\u0642\u0627\u0631\u0628 \u0623\u0648 \u0627\u0644\u062a\u0639\u062b\u0631 \u0641\u064a \u0627\u0644\u0623\u0645\u062b\u0644 \u0627\u0644\u0645\u062d\u0644\u064a. \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0624\u062f\u064a \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0642\u0648\u0627\u0639\u062f \u0627\u0644\u062a\u062d\u062f\u064a\u062b \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629 \u0648\u0623\u0633\u0627\u0644\u064a\u0628 \u0627\u0644\u062a\u0646\u0638\u064a\u0645 \u0625\u0644\u0649 \u062a\u062e\u0641\u064a\u0641 \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0643\u0644\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u062a\u062c\u0647\u064a\u0632 \u0627\u0644\u0632\u0627\u0626\u062f:<\/strong> \u0639\u0646\u062f \u0627\u0633\u062a\u062e\u062f\u0627\u0645 NMF \u0644\u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0627\u0644\u0645\u064a\u0632\u0627\u062a\u060c \u0647\u0646\u0627\u0643 \u062e\u0637\u0631 \u0627\u0644\u0625\u0641\u0631\u0627\u0637 \u0641\u064a \u0645\u0644\u0627\u0621\u0645\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a. \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0633\u0627\u0639\u062f \u062a\u0642\u0646\u064a\u0627\u062a \u0645\u062b\u0644 \u0627\u0644\u062a\u0646\u0638\u064a\u0645 \u0648\u0627\u0644\u062a\u062d\u0642\u0642 \u0627\u0644\u0645\u062a\u0628\u0627\u062f\u0644 \u0641\u064a \u0645\u0646\u0639 \u0627\u0644\u062a\u062c\u0647\u064a\u0632 \u0627\u0644\u0632\u0627\u0626\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u062d\u062c\u064a\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a:<\/strong> NMF \u062d\u0633\u0627\u0633 \u0644\u062d\u062c\u0645 \u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0625\u062f\u062e\u0627\u0644. \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0624\u062f\u064a \u0642\u064a\u0627\u0633 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0628\u0634\u0643\u0644 \u0635\u062d\u064a\u062d \u0642\u0628\u0644 \u062a\u0637\u0628\u064a\u0642 NMF \u0625\u0644\u0649 \u062a\u062d\u0633\u064a\u0646 \u0623\u062f\u0627\u0626\u0647\u0627.<\/p>\n<\/li>\n<li>\n<p><strong>\u0628\u064a\u0627\u0646\u0627\u062a \u0645\u0641\u0642\u0648\u062f\u0629:<\/strong> \u062a\u062a\u0639\u0627\u0645\u0644 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a NMF \u0645\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u0641\u0642\u0648\u062f\u0629\u060c \u0644\u0643\u0646 \u0648\u062c\u0648\u062f \u0639\u062f\u062f \u0643\u0628\u064a\u0631 \u062c\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u0641\u0642\u0648\u062f\u0629 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u062a\u062d\u0644\u064a\u0644 \u063a\u064a\u0631 \u062f\u0642\u064a\u0642. \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0636\u0645\u064a\u0646 \u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u0641\u0642\u0648\u062f\u0629 \u0628\u0634\u0643\u0644 \u0641\u0639\u0627\u0644.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0648\u0645\u0642\u0627\u0631\u0646\u0627\u062a \u0623\u062e\u0631\u0649 \u0645\u0639 \u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0645\u0645\u0627\u062b\u0644\u0629 \u0641\u064a \u0634\u0643\u0644 \u062c\u062f\u0627\u0648\u0644 \u0648\u0642\u0648\u0627\u0626\u0645.<\/h2>\n<p>\u064a\u0648\u062c\u062f \u0623\u062f\u0646\u0627\u0647 \u062c\u062f\u0648\u0644 \u0645\u0642\u0627\u0631\u0646\u0629 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u0645\u0639 \u062a\u0642\u0646\u064a\u0627\u062a \u0623\u062e\u0631\u0649 \u0645\u0645\u0627\u062b\u0644\u0629:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u062a\u0642\u0646\u064a\u0629<\/th>\n<th>\u0642\u064a\u062f \u0639\u062f\u0645 \u0627\u0644\u0633\u0644\u0628\u064a\u0629<\/th>\n<th>\u0627\u0644\u0642\u0627\u0628\u0644\u064a\u0629 \u0644\u0644\u062a\u0641\u0633\u064a\u0631<\/th>\n<th>\u0645\u062a\u0646\u0627\u062b\u0631\u0629<\/th>\n<th>\u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u0641\u0642\u0648\u062f\u0629<\/th>\n<th>\u0627\u0641\u062a\u0631\u0627\u0636 \u0627\u0644\u062e\u0637\u064a\u0629<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 (NMF)<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0639\u0627\u0644\u064a<\/td>\n<td>\u062e\u064a\u0627\u0631\u064a<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u062e\u0637\u064a<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 (PCA)<\/td>\n<td>\u0644\u0627<\/td>\n<td>\u0642\u0644\u064a\u0644<\/td>\n<td>\u0644\u0627<\/td>\n<td>\u0644\u0627<\/td>\n<td>\u062e\u0637\u064a<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 (ICA)<\/td>\n<td>\u0644\u0627<\/td>\n<td>\u0642\u0644\u064a\u0644<\/td>\n<td>\u062e\u064a\u0627\u0631\u064a<\/td>\n<td>\u0644\u0627<\/td>\n<td>\u062e\u0637\u064a<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u062e\u0635\u064a\u0635 \u062f\u0631\u064a\u0634\u0644\u064a\u062a \u0627\u0644\u0643\u0627\u0645\u0646 (LDA)<\/td>\n<td>\u0644\u0627<\/td>\n<td>\u0639\u0627\u0644\u064a<\/td>\n<td>\u0645\u062a\u0646\u0627\u062b\u0631<\/td>\n<td>\u0644\u0627<\/td>\n<td>\u062e\u0637\u064a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li>\n<p><strong>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 (NMF):<\/strong> \u064a\u0641\u0631\u0636 NMF \u0642\u064a\u0648\u062f\u064b\u0627 \u063a\u064a\u0631 \u0633\u0644\u0628\u064a\u0629 \u0639\u0644\u0649 \u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633 \u0648\u0627\u0644\u0645\u0639\u0627\u0645\u0644\u060c \u0645\u0645\u0627 \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0639\u0644\u0649 \u0623\u0633\u0627\u0633 \u0627\u0644\u0623\u062c\u0632\u0627\u0621 \u0648\u0642\u0627\u0628\u0644 \u0644\u0644\u062a\u0641\u0633\u064a\u0631.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 (PCA):<\/strong> PCA \u0647\u064a \u062a\u0642\u0646\u064a\u0629 \u062e\u0637\u064a\u0629 \u062a\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0648\u062a\u0648\u0641\u0631 \u0645\u0643\u0648\u0646\u0627\u062a \u0645\u062a\u0639\u0627\u0645\u062f\u0629\u060c \u0648\u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u0636\u0645\u0646 \u0625\u0645\u0643\u0627\u0646\u064a\u0629 \u0627\u0644\u062a\u0641\u0633\u064a\u0631.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 (ICA):<\/strong> \u064a\u0647\u062f\u0641 ICA \u0625\u0644\u0649 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u0643\u0648\u0646\u0627\u062a \u0645\u0633\u062a\u0642\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u064b\u0627\u060c \u0648\u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0623\u0643\u062b\u0631 \u0642\u0627\u0628\u0644\u064a\u0629 \u0644\u0644\u062a\u0641\u0633\u064a\u0631 \u0645\u0646 PCA \u0648\u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u0636\u0645\u0646 \u0627\u0644\u062a\u0646\u0627\u062b\u0631.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u062e\u0635\u064a\u0635 \u062f\u0631\u064a\u0634\u0644\u064a\u062a \u0627\u0644\u0643\u0627\u0645\u0646 (LDA):<\/strong> LDA \u0647\u0648 \u0646\u0645\u0648\u0630\u062c \u0627\u062d\u062a\u0645\u0627\u0644\u064a \u064a\u0633\u062a\u062e\u062f\u0645 \u0644\u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0645\u0648\u0636\u0648\u0639 \u0641\u064a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0646\u0635\u064a\u0629. \u0625\u0646\u0647 \u064a\u0648\u0641\u0631 \u062a\u0645\u062b\u064a\u0644\u0627\u064b \u0645\u062a\u0646\u0627\u062b\u0631\u064b\u0627 \u0648\u0644\u0643\u0646\u0647 \u064a\u0641\u062a\u0642\u0631 \u0625\u0644\u0649 \u0627\u0644\u0642\u064a\u0648\u062f \u063a\u064a\u0631 \u0627\u0644\u0633\u0644\u0628\u064a\u0629.<\/p>\n<\/li>\n<\/ul>\n<h2>\u0648\u062c\u0647\u0627\u062a \u0646\u0638\u0631 \u0648\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0644\u0628\u064a\u0629 (NMF).<\/h2>\n<p>\u0644\u0627 \u064a\u0632\u0627\u0644 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u0645\u062c\u0627\u0644\u064b\u0627 \u0646\u0634\u0637\u064b\u0627 \u0644\u0644\u0628\u062d\u062b \u0648\u0627\u0644\u062a\u0637\u0648\u064a\u0631. \u0628\u0639\u0636 \u0648\u062c\u0647\u0627\u062a \u0627\u0644\u0646\u0638\u0631 \u0648\u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644\u064a\u0629 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0640 NMF \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<ol>\n<li>\n<p><strong>\u062a\u0643\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0639\u0645\u064a\u0642:<\/strong> \u0642\u062f \u064a\u0624\u062f\u064a \u062f\u0645\u062c NMF \u0645\u0639 \u0628\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0639\u0645\u064a\u0642 \u0625\u0644\u0649 \u062a\u0639\u0632\u064a\u0632 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0627\u0644\u0645\u064a\u0632\u0627\u062a \u0648\u0642\u0627\u0628\u0644\u064a\u0629 \u062a\u0641\u0633\u064a\u0631 \u0627\u0644\u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0639\u0645\u064a\u0642\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0642\u0648\u064a\u0629 \u0648\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062a\u0637\u0648\u064a\u0631:<\/strong> \u062a\u0631\u0643\u0632 \u0627\u0644\u0623\u0628\u062d\u0627\u062b \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629 \u0639\u0644\u0649 \u062a\u0637\u0648\u064a\u0631 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a NMF \u0642\u0648\u064a\u0629 \u0648\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062a\u0637\u0648\u064a\u0631 \u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0648\u0627\u0633\u0639\u0629 \u0627\u0644\u0646\u0637\u0627\u0642 \u0628\u0643\u0641\u0627\u0621\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0627\u0644\u0645\u062c\u0627\u0644:<\/strong> \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0624\u062f\u064a \u062a\u0635\u0645\u064a\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a NMF \u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0645\u062d\u062f\u062f\u0629\u060c \u0645\u062b\u0644 \u0627\u0644\u062a\u0635\u0648\u064a\u0631 \u0627\u0644\u0637\u0628\u064a\u060c \u0648\u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0645\u0646\u0627\u062e\u060c \u0648\u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0627\u062c\u062a\u0645\u0627\u0639\u064a\u0629\u060c \u0625\u0644\u0649 \u0625\u0637\u0644\u0627\u0642 \u0631\u0624\u0649 \u0648\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u062c\u062f\u064a\u062f\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u0633\u0631\u064a\u0639 \u0627\u0644\u0623\u062c\u0647\u0632\u0629:<\/strong> \u0645\u0639 \u062a\u0642\u062f\u0645 \u0627\u0644\u0623\u062c\u0647\u0632\u0629 \u0627\u0644\u0645\u062a\u062e\u0635\u0635\u0629 (\u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0648\u062d\u062f\u0627\u062a \u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0631\u0633\u0648\u0645\u0627\u062a \u0648\u0648\u062d\u062f\u0627\u062a TPU)\u060c \u064a\u0645\u0643\u0646 \u062a\u0633\u0631\u064a\u0639 \u062d\u0633\u0627\u0628\u0627\u062a NMF \u0628\u0634\u0643\u0644 \u0643\u0628\u064a\u0631\u060c \u0645\u0645\u0627 \u064a\u062a\u064a\u062d \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0641\u064a \u0627\u0644\u0648\u0642\u062a \u0627\u0644\u0641\u0639\u0644\u064a.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u062a\u0639\u0644\u0645 \u0639\u0628\u0631 \u0627\u0644\u0625\u0646\u062a\u0631\u0646\u062a \u0648\u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0645\u062a\u0632\u0627\u064a\u062f:<\/strong> \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0633\u0645\u062d \u0627\u0644\u0628\u062d\u062b \u0639\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a NMF \u0627\u0644\u0645\u062a\u0632\u0627\u064a\u062f\u0629 \u0639\u0628\u0631 \u0627\u0644\u0625\u0646\u062a\u0631\u0646\u062a \u0628\u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0645\u0633\u062a\u0645\u0631 \u0648\u0627\u0644\u062a\u0643\u064a\u0641 \u0645\u0639 \u062a\u062f\u0641\u0642\u0627\u062a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a\u0629.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0643\u064a\u0641 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0623\u0648 \u0631\u0628\u0637\u0647\u0627 \u0628\u0639\u0627\u0645\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 (NMF).<\/h2>\n<p>\u062a\u0644\u0639\u0628 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u062f\u0648\u0631\u064b\u0627 \u062d\u0627\u0633\u0645\u064b\u0627 \u0641\u064a \u0627\u0644\u0627\u062a\u0635\u0627\u0644 \u0639\u0628\u0631 \u0627\u0644\u0625\u0646\u062a\u0631\u0646\u062a\u060c \u062d\u064a\u062b \u062a\u0639\u0645\u0644 \u0643\u0648\u0633\u064a\u0637 \u0628\u064a\u0646 \u0627\u0644\u0639\u0645\u0644\u0627\u0621 \u0648\u0627\u0644\u062e\u0648\u0627\u062f\u0645. \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 NMF \u0644\u0627 \u064a\u0631\u062a\u0628\u0637 \u0628\u0634\u0643\u0644 \u0645\u0628\u0627\u0634\u0631 \u0628\u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629\u060c \u0625\u0644\u0627 \u0623\u0646\u0647 \u064a\u0645\u0643\u0646\u0647 \u0627\u0644\u0627\u0633\u062a\u0641\u0627\u062f\u0629 \u0628\u0634\u0643\u0644 \u063a\u064a\u0631 \u0645\u0628\u0627\u0634\u0631 \u0645\u0646 \u062d\u0627\u0644\u0627\u062a \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ol>\n<li>\n<p><strong>\u0627\u0644\u062a\u062e\u0632\u064a\u0646 \u0627\u0644\u0645\u0624\u0642\u062a \u0639\u0644\u0649 \u0634\u0628\u0643\u0629 \u0627\u0644\u0625\u0646\u062a\u0631\u0646\u062a:<\/strong> \u062a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0627\u0644\u062a\u062e\u0632\u064a\u0646 \u0627\u0644\u0645\u0624\u0642\u062a \u0639\u0644\u0649 \u0627\u0644\u0648\u064a\u0628 \u0644\u062a\u062e\u0632\u064a\u0646 \u0627\u0644\u0645\u062d\u062a\u0648\u0649 \u0627\u0644\u0630\u064a \u064a\u062a\u0645 \u0627\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u064a\u0647 \u0628\u0634\u0643\u0644 \u0645\u062a\u0643\u0631\u0631 \u0645\u062d\u0644\u064a\u064b\u0627. \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 NMF \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u062d\u062a\u0648\u0649 \u0627\u0644\u0623\u0643\u062b\u0631 \u0635\u0644\u0629 \u0648\u063a\u0646\u064a \u0628\u0627\u0644\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u0644\u0644\u062a\u062e\u0632\u064a\u0646 \u0627\u0644\u0645\u0624\u0642\u062a\u060c \u0645\u0645\u0627 \u064a\u062d\u0633\u0646 \u0643\u0641\u0627\u0621\u0629 \u0622\u0644\u064a\u0629 \u0627\u0644\u062a\u062e\u0632\u064a\u0646 \u0627\u0644\u0645\u0624\u0642\u062a.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u062d\u0644\u064a\u0644 \u0633\u0644\u0648\u0643 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645:<\/strong> \u064a\u0645\u0643\u0646 \u0644\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0627\u0644\u062a\u0642\u0627\u0637 \u0628\u064a\u0627\u0646\u0627\u062a \u0633\u0644\u0648\u0643 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u060c \u0645\u062b\u0644 \u0637\u0644\u0628\u0627\u062a \u0627\u0644\u0648\u064a\u0628 \u0648\u0623\u0646\u0645\u0627\u0637 \u0627\u0644\u062a\u0635\u0641\u062d. \u064a\u0645\u0643\u0646 \u0628\u0639\u062f \u0630\u0644\u0643 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 NMF \u0644\u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0627\u0644\u0645\u064a\u0632\u0627\u062a \u0627\u0644\u0643\u0627\u0645\u0646\u0629 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0645\u0645\u0627 \u064a\u0633\u0627\u0639\u062f \u0641\u064a \u062a\u062d\u062f\u064a\u062f \u0645\u0644\u0641\u0627\u062a \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645 \u0648\u062a\u0633\u0644\u064a\u0645 \u0627\u0644\u0645\u062d\u062a\u0648\u0649 \u0627\u0644\u0645\u0633\u062a\u0647\u062f\u0641.<\/p>\n<\/li>\n<li>\n<p><strong>\u0625\u0643\u062a\u0634\u0627\u0641 \u0639\u064a\u0628 \u062e\u0644\u0642\u064a:<\/strong> \u064a\u0645\u0643\u0646 \u062a\u0637\u0628\u064a\u0642 NMF \u0644\u062a\u062d\u0644\u064a\u0644 \u0623\u0646\u0645\u0627\u0637 \u062d\u0631\u0643\u0629 \u0627\u0644\u0645\u0631\u0648\u0631 \u0627\u0644\u062a\u064a \u062a\u0645\u0631 \u0639\u0628\u0631 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629. \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0623\u0646\u0645\u0627\u0637 \u063a\u064a\u0631 \u0627\u0644\u0645\u0639\u062a\u0627\u062f\u0629\u060c \u064a\u0645\u0643\u0646 \u0644\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0627\u0643\u062a\u0634\u0627\u0641 \u0627\u0644\u062a\u0647\u062f\u064a\u062f\u0627\u062a \u0627\u0644\u0623\u0645\u0646\u064a\u0629 \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629 \u0648\u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u0634\u0627\u0630\u0629 \u0641\u064a \u0646\u0634\u0627\u0637 \u0627\u0644\u0634\u0628\u0643\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u0635\u0641\u064a\u0629 \u0627\u0644\u0645\u062d\u062a\u0648\u0649 \u0648\u062a\u0635\u0646\u064a\u0641\u0647:<\/strong> \u064a\u0645\u0643\u0646 \u0644\u0640 NMF \u0645\u0633\u0627\u0639\u062f\u0629 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0641\u064a \u062a\u0635\u0641\u064a\u0629 \u0627\u0644\u0645\u062d\u062a\u0648\u0649 \u0648\u062a\u0635\u0646\u064a\u0641\u0647\u060c \u0645\u0645\u0627 \u064a\u0633\u0627\u0639\u062f \u0639\u0644\u0649 \u062d\u0638\u0631 \u0623\u0648 \u0627\u0644\u0633\u0645\u0627\u062d \u0628\u0623\u0646\u0648\u0627\u0639 \u0645\u0639\u064a\u0646\u0629 \u0645\u0646 \u0627\u0644\u0645\u062d\u062a\u0648\u0649 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0645\u064a\u0632\u0627\u062a\u0647\u0627 \u0648\u0623\u0646\u0645\u0627\u0637\u0647\u0627.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0631\u0648\u0627\u0628\u0637 \u0630\u0627\u062a \u0639\u0644\u0627\u0642\u0629<\/h2>\n<p>\u0644\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u062d\u0648\u0644 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 (NMF)\u060c \u064a\u0631\u062c\u0649 \u0627\u0644\u0631\u062c\u0648\u0639 \u0625\u0644\u0649 \u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ol>\n<li>\n<p><a href=\"https:\/\/www.nature.com\/articles\/44565\" target=\"_new\" rel=\"noopener nofollow\">\u062a\u0639\u0644\u0645 \u0623\u062c\u0632\u0627\u0621 \u0627\u0644\u0643\u0627\u0626\u0646\u0627\u062a \u0639\u0646 \u0637\u0631\u064a\u0642 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u2013 \u062f\u0627\u0646\u064a\u064a\u0644 \u062f. \u0644\u064a \u0648\u0647. \u0633\u064a\u0628\u0627\u0633\u062a\u064a\u0627\u0646 \u0633\u064a\u0648\u0646\u062c<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Non-negative_matrix_factorization\" target=\"_new\" rel=\"noopener nofollow\">\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 - \u0648\u064a\u0643\u064a\u0628\u064a\u062f\u064a\u0627<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/www.datacamp.com\/community\/tutorials\/tutorial-nmf-python\" target=\"_new\" rel=\"noopener nofollow\">\u0645\u0642\u062f\u0645\u0629 \u0625\u0644\u0649 \u0639\u0648\u0627\u0645\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629: \u062f\u0644\u064a\u0644 \u0634\u0627\u0645\u0644 \u2013 Datacamp<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/towardsdatascience.com\/nmf-unsupervised-feature-extraction-e1582b4e5afe\" target=\"_new\" rel=\"noopener nofollow\">\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629: \u0641\u0647\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0648\u0643\u064a\u0641 \u062a\u0639\u0645\u0644 \u2013 \u0645\u062a\u0648\u0633\u0637<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/arxiv.org\/abs\/2002.01460\" target=\"_new\" rel=\"noopener nofollow\">\u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0639\u0645\u064a\u0642 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0639\u0627\u0645\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u063a\u064a\u0631 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u0644\u062a\u0631\u0645\u064a\u0632 \u0627\u0644\u0635\u0648\u0631 \u2013 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\/ar\/wp-json\/wp\/v2\/wiki\/478216","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki\/478216\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/media\/469015"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/media?parent=478216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}