{"id":15124,"date":"2024-01-09T00:02:36","date_gmt":"2024-01-08T20:32:36","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/"},"modified":"2024-01-09T00:02:36","modified_gmt":"2024-01-08T20:32:36","slug":"%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/","title":{"rendered":"\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc: \u062a\u0626\u0648\u0631\u06cc \u0648 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0628\u0627 Scikit-Learn"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0633\u0631\u0641\u0635\u0644\u0647\u0627\u06cc \u0645\u0637\u0644\u0628<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d9%85%d8%b9%d8%b1%d9%81%db%8c\" >\u0645\u0639\u0631\u0641\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d8%b7%d8%b1%d8%ad_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%db%8c%da%a9_%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87_%da%86%db%8c%d8%b3%d8%aa%d8%9f\" >\u0637\u0631\u062d \u062a\u0635\u0627\u062f\u0641\u06cc \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0686\u06cc\u0633\u062a\u061f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%db%8c%da%a9_%d9%85%d8%ab%d8%a7%d9%84_%d8%b3%d8%a7%d8%af%d9%87\" >\u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0633\u0627\u062f\u0647<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d9%84%d9%85_%d8%ac%d8%a7%d9%86%d8%b3%d9%88%d9%86-%d9%84%db%8c%d9%86%d8%af%d9%86_%d8%a7%d8%b4%d8%aa%d8%b1%d8%a7%d9%88%d8%b3\" >\u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d8%aa%d8%b9%db%8c%db%8c%d9%86_%d8%ac%d9%87%d8%a7%d8%aa_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%d9%85%d8%a7%d8%aa%d8%b1%db%8c%d8%b3_%d9%be%d8%b1%d9%88%d8%ac%da%a9%d8%b4%d9%86\" >\u062a\u0639\u06cc\u06cc\u0646 \u062c\u0647\u0627\u062a \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u067e\u0631\u0648\u062c\u06a9\u0634\u0646<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d8%b7%d8%b1%d8%ad_%d8%b1%db%8c%d8%b2%db%8c_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_scikit-learn\" >\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d8%aa%d8%b9%db%8c%db%8c%d9%86_%d8%ad%d8%af%d8%a7%d9%82%d9%84_%d8%aa%d8%b9%d8%af%d8%a7%d8%af_%d8%a7%d8%a8%d8%b9%d8%a7%d8%af_%d8%a7%d8%b2_%d8%b7%d8%b1%db%8c%d9%82_%d9%84%d9%85_%d8%ac%d8%a7%d9%86%d8%b3%d9%88%d9%86_%d9%84%db%8c%d9%86%d8%af%d9%86_%d8%a7%d8%b4%d8%aa%d8%b1%d8%a7%d9%88%d8%b3\" >\u062a\u0639\u06cc\u06cc\u0646 \u062d\u062f\u0627\u0642\u0644 \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d8%aa%d8%a8%d8%af%db%8c%d9%84_%d8%af%d8%a7%d8%af%d9%87_%d9%87%d8%a7\" >\u062a\u0628\u062f\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d9%be%db%8c%d8%b4_%d8%a8%db%8c%d9%86%db%8c_%d9%87%d8%a7%db%8c_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%d8%b9%d9%85%d9%84%db%8c_%d8%a8%d8%a7_%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87_%d8%ac%d9%84%d8%af_1_%d9%87%d8%b3%d8%aa%d9%87_%d8%b1%d9%88%db%8c%d8%aa%d8%b1%d8%b2\" >\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0639\u0645\u0644\u06cc \u0628\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062c\u0644\u062f 1 \u0647\u0633\u062a\u0647 \u0631\u0648\u06cc\u062a\u0631\u0632<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87_%d8%b1%d9%88%db%8c%d8%aa%d8%b1%d8%b2_%d8%b7%d8%b1%d8%ad_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%da%af%d8%a7%d9%88%d8%b3%db%8c\" >\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0648\u06cc\u062a\u0631\u0632: \u0637\u0631\u062d \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87_%d8%b1%d9%88%db%8c%d8%aa%d8%b1%d8%b2_%d8%b7%d8%b1%d8%ad_%d8%b1%db%8c%d8%b2%db%8c_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%d9%be%d8%b1%d8%a7%da%a9%d9%86%d8%af%d9%87\" >\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0648\u06cc\u062a\u0631\u0632: \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b7%d8%b1%d8%ad-%d8%b1%db%8c%d8%b2%db%8c-%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c-%d8%aa%d8%a6%d9%88%d8%b1%db%8c-%d9%88-%d9%be%db%8c%d8%a7%d8%af%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87_%da%af%db%8c%d8%b1%db%8c\" >\u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc<\/a><\/li><\/ul><\/nav><\/div>\n<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 11<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<h2 id=\"introduction\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%d8%b1%d9%81%db%8c\"><\/span>\u0645\u0639\u0631\u0641\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627 \u0645\u0642\u062f\u0645\u0647\u200c\u0627\u06cc \u0639\u0645\u06cc\u0642 \u0628\u0631\u0627\u06cc \u062a\u06a9\u0646\u06cc\u06a9 \u06a9\u0627\u0647\u0634 \u0627\u0628\u0639\u0627\u062f \u0628\u062f\u0648\u0646 \u0646\u0638\u0627\u0631\u062a \u0627\u0633\u062a \u06a9\u0647 \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f <strong><em>\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc<\/em><\/strong>.  \u06cc\u06a9 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0631\u0627\u06cc \u06a9\u0627\u0647\u0634 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0648 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f \u0648 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0622\u0633\u0627\u0646 \u062a\u0631 \u06a9\u0646\u062f process \u0648 \u062a\u062c\u0633\u0645 \u06a9\u0646\u06cc\u062f.  \u0647\u0645\u0686\u0646\u06cc\u0646 \u06cc\u06a9 \u062a\u06a9\u0646\u06cc\u06a9 \u067e\u06cc\u0634 \u067e\u0631\u062f\u0627\u0632\u0634 \u0628\u0631\u0627\u06cc \u0622\u0645\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0648\u0631\u0648\u062f\u06cc \u0628\u0647 \u06cc\u06a9 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u06a9\u0646\u0646\u062f\u0647 \u06cc\u0627 \u06cc\u06a9 \u0631\u06af\u0631\u0633\u06cc\u0648\u0646 \u0627\u0633\u062a.<\/p>\n<blockquote>\n<p><strong>\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc<\/strong> \u0628\u0647 \u0637\u0648\u0631 \u0645\u0639\u0645\u0648\u0644 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0628\u0639\u062f\u06cc\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u062a\u06a9\u0646\u06cc\u06a9 \u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0645\u0627\u0646\u0646\u062f <strong>\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0627\u062c\u0632\u0627\u06cc \u0627\u0635\u0644\u06cc (PCA)<\/strong> \u0646\u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0639\u062f\u0627\u0644\u062a \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u062f.<\/p>\n<\/blockquote>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627\u060c \u0645\u0627 \u0628\u0647 \u062c\u0632\u0626\u06cc\u0627\u062a \u0622\u0646 \u062e\u0648\u0627\u0647\u06cc\u0645 \u067e\u0631\u062f\u0627\u062e\u062a <strong><em>\u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633<\/em><\/strong>\u060c \u06a9\u0647 \u067e\u0627\u06cc\u0647 \u0631\u06cc\u0627\u0636\u06cc \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0631\u0627 \u0645\u06cc \u06af\u0630\u0627\u0631\u062f.  \u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0646\u0634\u0627\u0646 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Scikit-Learn Python Projection \u062a\u0635\u0627\u062f\u0641\u06cc \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 \u0648 \u0627\u0632 \u0622\u0646 \u0628\u0631\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0648\u0631\u0648\u062f\u06cc \u0628\u0647 \u0641\u0636\u0627\u06cc\u06cc \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u06a9\u0645\u062a\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645.<\/p>\n<blockquote>\n<p><strong>\u062a\u0626\u0648\u0631\u06cc \u0646\u0638\u0631\u06cc\u0647 \u0627\u0633\u062a \u0648 \u0639\u0645\u0644 \u0639\u0645\u0644 \u0627\u0633\u062a<\/strong>.  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u062a\u0635\u0648\u06cc\u0631 \u0639\u0645\u0644\u06cc\u060c \u0645\u0627 \u0622\u0646 \u0631\u0627 \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.jmlr.org\/papers\/volume5\/lewis04a\/lewis04a.pdf\">\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062c\u0644\u062f \u0627\u0648\u0644 \u0631\u0648\u06cc\u062a\u0631\u0632<\/a>\u060c \u0648 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0648 \u0637\u0631\u062d \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0631\u0627 \u0631\u0648\u06cc \u0622\u0646 \u0627\u0639\u0645\u0627\u0644 \u06a9\u0646\u06cc\u062f.<\/p>\n<\/blockquote>\n<h2 id=\"whatisarandomprojectionofadataset\"><span class=\"ez-toc-section\" id=\"%d8%b7%d8%b1%d8%ad_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%db%8c%da%a9_%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87_%da%86%db%8c%d8%b3%d8%aa%d8%9f\"><\/span>\u0637\u0631\u062d \u062a\u0635\u0627\u062f\u0641\u06cc \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0686\u06cc\u0633\u062a\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u0647 \u0632\u0628\u0627\u0646 \u0633\u0627\u062f\u0647:<\/p>\n<blockquote>\n<p>\u0641\u0631\u0627\u0641\u06a9\u0646\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06cc\u06a9 \u0631\u0648\u0634 \u0627\u0633\u062a <strong>\u06a9\u0627\u0647\u0634 \u0627\u0628\u0639\u0627\u062f<\/strong> \u0648 <strong>\u062a\u062c\u0633\u0645 \u062f\u0627\u062f\u0647 \u0647\u0627<\/strong> \u06a9\u0647 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u0628\u0627\u0644\u0627 \u0631\u0627 \u0633\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<\/blockquote>\n<p>\u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u0647\u0631 \u0646\u0642\u0637\u0647 \u062f\u0627\u062f\u0647 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u062c\u0647\u062a \u0647\u0627 \u0628\u0647 \u0637\u0648\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0634\u062f\u0647\u060c \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062c\u062f\u06cc\u062f \u062a\u0648\u0644\u06cc\u062f \u0645\u06cc \u06a9\u0646\u062f.  \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u062f\u0627\u062f\u0647 \u0645\u0646\u0641\u0631\u062f \u0628\u0631 \u0631\u0648\u06cc \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0627\u0632 \u0646\u0638\u0631 \u0631\u06cc\u0627\u0636\u06cc \u0645\u0639\u0627\u062f\u0644 \u06af\u0631\u0641\u062a\u0646 \u0622\u0646 \u0627\u0633\u062a <strong>\u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0646\u0642\u0637\u0647 \u0628\u0627 \u0628\u0631\u062f\u0627\u0631<\/strong>.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-1.png\" alt=\"\u062a\u0635\u0648\u06cc\u0631 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc\" title=\"\"><\/p>\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0627\u062f\u0647 \\(X\\) \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \\(mxn\\) \u0648 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \\(dxn\\) \\(R\\) \u06a9\u0647 \u0633\u062a\u0648\u0646 \u0647\u0627\u06cc \u0622\u0646 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u062c\u0647\u062a \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u0646\u062f\u060c \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \\(X\\) \u0628\u0627 \\(X_p\\).<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <msub>\n    <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n    <mi>\u067e<\/mi>\n  <\/msub>\n  <mo>=<\/mo>\n  <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <mi>\u0622\u0631<\/mi>\n<\/math><\/p>\n<p>\u0647\u0631 \u0628\u0631\u062f\u0627\u0631 \u06a9\u0647 \u06cc\u06a9 \u062c\u0647\u062a \u062a\u0635\u0627\u062f\u0641\u06cc \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u062f\u0627\u0631\u0627\u06cc \u0627\u0628\u0639\u0627\u062f \\(n\\) \u0627\u0633\u062a \u06a9\u0647 \u0645\u0627\u0646\u0646\u062f \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u062f\u0627\u062f\u0647 \\(X\\) \u0627\u0633\u062a.  \u0627\u06af\u0631 \u062c\u0647\u062a\u200c\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \\(d\\) \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645\u060c \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0628\u0647 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062a\u0628\u062f\u06cc\u0644\u200c\u0634\u062f\u0647 \u0627\u0628\u0639\u0627\u062f\u06cc \\(d\\) \u0645\u06cc\u200c\u0631\u0633\u06cc\u0645.  \u0628\u0631\u0627\u06cc \u0647\u062f\u0641 \u0627\u06cc\u0646 \u0622\u0645\u0648\u0632\u0634\u060c \u0686\u0646\u062f \u0646\u0645\u0627\u062f \u0631\u0627 \u0627\u0635\u0644\u0627\u062d \u0645\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<ul>\n<li><code>m<\/code>: \u06a9\u0644 \u0646\u0642\u0627\u0637 \u0646\u0645\u0648\u0646\u0647\/\u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0648\u0631\u0648\u062f\u06cc.<\/li>\n<li><code>n<\/code>: \u0645\u062c\u0645\u0648\u0639 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\/\u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0648\u0631\u0648\u062f\u06cc.  \u0647\u0645\u0686\u0646\u06cc\u0646 \u0627\u0628\u0639\u0627\u062f \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0627\u0635\u0644\u06cc \u0627\u0633\u062a.<\/li>\n<li><code>d<\/code>: \u0627\u0628\u0639\u0627\u062f \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f\u0647.<\/li>\n<\/ul>\n<p>\u0627\u06cc\u062f\u0647 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0634\u0628\u06cc\u0647 \u0628\u0647 <strong>\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0627\u062c\u0632\u0627\u06cc \u0627\u0635\u0644\u06cc (PCA)<\/strong>\u060c \u0627\u0633\u0627\u0633\u0627  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u062f\u0631 PCA\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u062f <strong>\u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0648\u06cc\u0698\u0647<\/strong>\u060c \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0627\u0632 \u0646\u0638\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0628\u0631\u0627\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u06af\u0631\u0627\u0646 \u0628\u0627\u0634\u062f.<\/p>\n<blockquote>\n<p>\u0647\u0646\u06af\u0627\u0645 \u0627\u0646\u062c\u0627\u0645 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc\u060c \u0628\u0631\u062f\u0627\u0631\u0647\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u0634\u0648\u0646\u062f \u0648 \u0622\u0646 \u0631\u0627 \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0627\u0631\u0622\u0645\u062f \u0645\u06cc \u06a9\u0646\u0646\u062f.  \u0646\u0627\u0645 <em>&#8220;\u0637\u0631\u062d \u0628\u06cc\u0646\u06cc&#8221;<\/em> \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0628\u0631\u062f\u0627\u0631\u0647\u0627 \u06a9\u0645\u06cc \u06af\u0645\u0631\u0627\u0647 \u06a9\u0646\u0646\u062f\u0647 \u0628\u0627\u0634\u062f <strong>\u0628\u0647 \u0635\u0648\u0631\u062a \u062a\u0635\u0627\u062f\u0641\u06cc<\/strong>\u060c \u0646\u0642\u0627\u0637 \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0632 \u0646\u0638\u0631 \u0631\u06cc\u0627\u0636\u06cc \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062f\u0631\u0633\u062a \u0646\u06cc\u0633\u062a\u0646\u062f \u0627\u0645\u0627 \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc \u0647\u0633\u062a\u0646\u062f.<\/p>\n<\/blockquote>\n<p>\u06a9\u0627\u0631 \u0628\u0627 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc\u06cc \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u06a9\u0627\u0647\u0634 \u06cc\u0627\u0641\u062a\u0647 \u0622\u0633\u0627\u0646 \u062a\u0631 \u0627\u0633\u062a.  \u0646\u0647 \u062a\u0646\u0647\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0622\u0646 \u0631\u0627 \u062a\u062c\u0633\u0645 \u06a9\u0631\u062f\u060c \u0628\u0644\u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u0622\u0646 \u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u067e\u06cc\u0634 \u067e\u0631\u062f\u0627\u0632\u0634 \u0646\u06cc\u0632 \u0628\u0631\u0627\u06cc \u06a9\u0627\u0647\u0634 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0627\u0635\u0644\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.<\/p>\n<h2 id=\"asimpleexample\"><span class=\"ez-toc-section\" id=\"%db%8c%da%a9_%d9%85%d8%ab%d8%a7%d9%84_%d8%b3%d8%a7%d8%af%d9%87\"><\/span>\u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0633\u0627\u062f\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0628\u0641\u0647\u0645\u06cc\u0645 \u062a\u0628\u062f\u06cc\u0644 \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f\u060c \u0645\u062b\u0627\u0644 \u0633\u0627\u062f\u0647 \u0632\u06cc\u0631 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc \u06af\u06cc\u0631\u06cc\u0645.<\/p>\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0645\u0627\u062a\u0631\u06cc\u0633 \u0648\u0631\u0648\u062f\u06cc \u0645\u0627 \\(X\\) \u062a\u0648\u0633\u0637:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>3<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>3<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p>\u0648 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0648\u0633\u0637:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u0622\u0631<\/mi>\n  <mo>=<\/mo>\n  <mfrac>\n    <mn>1<\/mn>\n    <mn>2<\/mn>\n  <\/mfrac>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p>\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc X \u0628\u0631 \u0631\u0648\u06cc R \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <msub>\n    <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n    <mi>\u067e<\/mi>\n  <\/msub>\n  <mo>=<\/mo>\n  <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <mi>\u0622\u0631<\/mi>\n  <mo>=<\/mo>\n  <mfrac>\n    <mn>1<\/mn>\n    <mn>2<\/mn>\n  <\/mfrac>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>6<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>4<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>4<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n<\/math><\/p>\n<blockquote>\n<p>\u0645\u0627 \u0628\u0627 \u0633\u0647 \u0627\u0645\u062a\u06cc\u0627\u0632 \u062f\u0631 \u06cc\u06a9 \u0634\u0631\u0648\u0639 \u06a9\u0631\u062f\u06cc\u0645 <strong>\u0641\u0636\u0627\u06cc \u0686\u0647\u0627\u0631 \u0628\u0639\u062f\u06cc<\/strong>\u060c \u0648 \u0628\u0627 \u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u0647\u0648\u0634\u0645\u0646\u062f\u0627\u0646\u0647 \u0628\u0647 \u0633\u0647 \u0646\u0642\u0637\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f\u0647 \u062f\u0631 a \u062e\u062a\u0645 \u0634\u062f <strong>\u0641\u0636\u0627\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc<\/strong>.<\/p>\n<\/blockquote>\n<p>\u0628\u0647 \u0628\u0631\u062e\u06cc \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0645\u0647\u0645 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \\(R\\) \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f.  \u0647\u0631 \u0633\u062a\u0648\u0646 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0648\u0627\u062d\u062f \u0627\u0633\u062a\u060c \u06cc\u0639\u0646\u06cc \u0647\u0646\u062c\u0627\u0631 \u0647\u0631 \u0633\u062a\u0648\u0646 \u06cc\u06a9 \u0627\u0633\u062a.  \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u062d\u0627\u0635\u0644\u0636\u0631\u0628 \u0646\u0642\u0637\u0647\u200c\u0627\u06cc \u062a\u0645\u0627\u0645 \u0633\u062a\u0648\u0646\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0647\u200c\u0635\u0648\u0631\u062a \u0632\u0648\u062c\u06cc \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647\u200c\u0627\u0646\u062f (\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f \u0641\u0642\u0637 \u0633\u062a\u0648\u0646 1 \u0648 \u0633\u062a\u0648\u0646 2) \u0635\u0641\u0631 \u0627\u0633\u062a\u060c \u06a9\u0647 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u0647\u0631 \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u0633\u062a\u0648\u0646 \u0645\u062a\u0639\u0627\u0645\u062f \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u0627\u06cc\u0646 \u0628\u0627\u0639\u062b \u0645\u06cc \u0634\u0648\u062f \u0645\u0627\u062a\u0631\u06cc\u0633\u060c an <strong><em>\u0645\u0627\u062a\u0631\u06cc\u0633 Orthonormal<\/em><\/strong>.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u062f\u0631 \u0645\u0648\u0631\u062f \u062a\u06a9\u0646\u06cc\u06a9 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u0646\u0628\u0627\u06cc\u062f \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u062a\u0639\u0627\u0631\u0641 \u0648\u0627\u0642\u0639\u06cc \u0628\u0627\u0634\u062f \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627 \u062f\u0631\u06af\u06cc\u0631 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u0645\u0648\u0641\u0642\u06cc\u062a \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u0628\u062a\u0646\u06cc \u0627\u0633\u062a \u0631\u0648\u06cc \u06cc\u06a9 <em>\u0639\u0627\u0644\u06cc<\/em> \u06cc\u0627\u0641\u062a\u0647 \u0631\u06cc\u0627\u0636\u06cc \u0645\u0639\u0631\u0648\u0641 \u0628\u0647 <strong><em>\u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u0646\u062f\u0646\u062f\u0631\u0627\u0633 \u0644\u06cc\u0645\u0645\u0627<\/em><\/strong>\u060c \u06a9\u0647 \u062f\u0631 \u0642\u0633\u0645\u062a \u0632\u06cc\u0631 \u0628\u0647 \u062a\u0641\u0635\u06cc\u0644 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a!<\/p>\n<h3 id=\"thejohnsonlindenstrausslemma\"><span class=\"ez-toc-section\" id=\"%d9%84%d9%85_%d8%ac%d8%a7%d9%86%d8%b3%d9%88%d9%86-%d9%84%db%8c%d9%86%d8%af%d9%86_%d8%a7%d8%b4%d8%aa%d8%b1%d8%a7%d9%88%d8%b3\"><\/span>\u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633 \u0645\u0628\u0646\u0627\u06cc \u0631\u06cc\u0627\u0636\u06cc \u0628\u0631\u0627\u06cc \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0633\u062a:<\/p>\n<blockquote>\n<p>\u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633 \u0628\u06cc\u0627\u0646 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0627\u06af\u0631 \u0646\u0642\u0627\u0637 \u062f\u0627\u062f\u0647 \u062f\u0631 a \u0642\u0631\u0627\u0631 \u0628\u06af\u06cc\u0631\u0646\u062f <strong>\u0641\u0636\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u0628\u0627\u0644\u0627<\/strong>\u060c \u0633\u067e\u0633 \u0686\u0646\u06cc\u0646 \u0646\u06a9\u0627\u062a\u06cc \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f \u0631\u0648\u06cc \u0633\u0627\u062f\u0647 <strong>\u062c\u0647\u062a \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0641\u0627\u0635\u0644\u0647 \u0647\u0627\u06cc \u0632\u0648\u062c\u06cc \u062e\u0648\u062f \u0631\u0627 \u062d\u0641\u0638 \u0645\u06cc \u06a9\u0646\u062f<\/strong>.<\/p>\n<\/blockquote>\n<p><em>\u062d\u0641\u0638 \u0645\u0633\u0627\u0641\u062a \u0647\u0627\u06cc \u0632\u0648\u062c\u06cc<\/em> \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0641\u0648\u0627\u0635\u0644 \u0632\u0648\u062c\u06cc \u0628\u06cc\u0646 \u0646\u0642\u0627\u0637 \u062f\u0631 \u0641\u0636\u0627\u06cc \u0627\u0635\u0644\u06cc \u06cc\u06a9\u0633\u0627\u0646 \u06cc\u0627 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u06cc\u06a9\u0633\u0627\u0646 \u0628\u0627 \u0641\u0627\u0635\u0644\u0647 \u0632\u0648\u062c\u06cc \u062f\u0631 \u0641\u0636\u0627\u06cc \u06a9\u0645\u200c\u0628\u0639\u062f \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc \u0634\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<blockquote>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0648 \u062e\u0648\u0634\u0647\u200c\u0647\u0627\u06cc \u062f\u0631\u0648\u0646 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u062f\u0631 \u0641\u0636\u0627\u06cc\u06cc \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u067e\u0627\u06cc\u06cc\u0646\u200c\u062a\u0631 \u0646\u06af\u0647\u062f\u0627\u0631\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0648 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0642\u0627\u0628\u0644\u200c\u062a\u0648\u062c\u0647\u06cc \u06a9\u0627\u0647\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f.<\/p>\n<\/blockquote>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627\u060c \u0645\u0627 \u0628\u0647 \u062a\u0641\u0627\u0648\u062a \u0641\u0627\u0635\u0644\u0647\u200c\u0647\u0627\u06cc \u0632\u0648\u062c\u06cc \u0648\u0627\u0642\u0639\u06cc \u0648 \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc\u200c\u0634\u062f\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 <strong><em>&#8220;\u0627\u0639\u0648\u062c\u0627\u062c&#8221;<\/em><\/strong>  \u062f\u0631 \u062f\u0627\u062f\u0647 \u0647\u0627 \u06a9\u0647 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062f\u0631 \u0641\u0636\u0627\u06cc \u062c\u062f\u06cc\u062f \u0645\u0639\u0631\u0641\u06cc \u0634\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<p>\u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u062f\u0646\u062f\u0631\u0648\u0633 \u0644\u0645\u0627 \u0646\u06cc\u0632 <strong><em>&#8220;\u0628\u06cc \u062e\u0637\u0631&#8221;<\/em><\/strong>  \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u0628\u0631\u0627\u06cc \u0646\u0645\u0627\u06cc\u0634 \u0646\u0642\u0627\u0637 \u062f\u0627\u062f\u0647 \u0628\u0631 \u0631\u0648\u06cc \u0622\u0646\u0647\u0627 \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647 \u062e\u0637\u0627 \/ \u0627\u0639\u0648\u062c\u0627\u062c \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647 \u062e\u0627\u0635\u06cc \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u06cc\u0627\u0641\u062a\u0646 \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u0645\u0648\u0631\u062f \u0646\u0638\u0631 \u0622\u0633\u0627\u0646 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>\u0627\u0632 \u0646\u0638\u0631 \u0631\u06cc\u0627\u0636\u06cc\u060c \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u06cc\u06a9 \u062c\u0641\u062a \u0646\u0642\u0637\u0647 \\((x_1,x_2)\\) \u0648 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0622\u0646\u0647\u0627 \\((x_1&#8242;,x_2&#8242;)\\) \u06cc\u06a9 <strong><em>eps-embedding<\/em><\/strong>:<\/p>\n<p>$$<br \/>(1 &#8211; \\epsilon) |x_1 &#8211; x_2|^2 < |x_1' - x_2'|^2 < (1 + \\epsilon) |x_1 - x_2|^2<br \/>$$<\/p>\n<p>\u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u062f\u0646\u0634\u062a\u0631\u0627\u0648\u0633 \u062d\u062f\u0627\u0642\u0644 \u0627\u0628\u0639\u0627\u062f \u0641\u0636\u0627\u06cc \u06a9\u0645 \u0628\u0639\u062f\u06cc \u0631\u0627 \u0645\u0634\u062e\u0635 \u0645\u06cc \u06a9\u0646\u062f \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647 \u0645\u0648\u0627\u0631\u062f \u0641\u0648\u0642 <em>eps-embedding<\/em> \u0646\u06af\u0647\u062f\u0627\u0631\u06cc \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<h3 id=\"determiningtherandomdirectionsoftheprojectionmatrix\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%b9%db%8c%db%8c%d9%86_%d8%ac%d9%87%d8%a7%d8%aa_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%d9%85%d8%a7%d8%aa%d8%b1%db%8c%d8%b3_%d9%be%d8%b1%d9%88%d8%ac%da%a9%d8%b4%d9%86\"><\/span>\u062a\u0639\u06cc\u06cc\u0646 \u062c\u0647\u0627\u062a \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u067e\u0631\u0648\u062c\u06a9\u0634\u0646<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062f\u0648 \u0631\u0648\u0634 \u0634\u0646\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/p>\n<ul>\n<li>\n<p><strong>\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc<\/strong>: \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0639\u0646\u0627\u0635\u0631 \u0628\u0647 \u0637\u0648\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0632 \u062a\u0648\u0632\u06cc\u0639 \u06af\u0627\u0648\u0633\u06cc \u0628\u0627 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0635\u0641\u0631 \u0633\u0627\u062e\u062a\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647<\/strong>: \u0627\u06cc\u0646 \u06cc\u06a9 \u0631\u0648\u0634 \u0646\u0633\u0628\u062a\u0627\u064b \u0633\u0627\u062f\u0647\u200c\u062a\u0631 \u0627\u0633\u062a\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0647\u0631 \u0645\u0624\u0644\u0641\u0647 \u0628\u0631\u062f\u0627\u0631\u06cc \u0645\u0642\u062f\u0627\u0631\u06cc \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647 {-k,0,+k} \u0627\u0633\u062a \u06a9\u0647 k \u06cc\u06a9 \u062b\u0627\u0628\u062a \u0627\u0633\u062a.  \u06cc\u06a9 \u0637\u0631\u062d \u0633\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u062a\u0648\u0644\u06cc\u062f \u0639\u0646\u0627\u0635\u0631 \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u06a9\u0647 \u0628\u0647 \u0622\u0646 \u0646\u06cc\u0632 \u0645\u06cc \u06af\u0648\u06cc\u0646\u062f <code>Achlioptas<\/code> \u0631\u0648\u0634 \u062a\u0646\u0638\u06cc\u0645 \\ (k = \\ sqrt 3 \\) \u0627\u0633\u062a:<\/p>\n<\/li>\n<\/ul>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <msub>\n    <mi>\u0622\u0631<\/mi>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mi>\u0645\u0646<\/mi>\n      <mi>j<\/mi>\n    <\/mrow>\n  <\/msub>\n  <mo>=<\/mo>\n  <msqrt>\n    <mn>3<\/mn>\n  <\/msqrt>\n  <mrow>\n    <mo>{<\/mo>\n    <mtable columnalign=\"left left\" rowspacing=\".2em\" columnspacing=\"1em\" displaystyle=\"false\">\n      <mtr>\n        <mtd>\n          <mo>+<\/mo>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mtext> \u0628\u0627 \u0627\u062d\u062a\u0645\u0627\u0644 <\/mtext>\n        <\/mtd>\n        <mtd>\n          <mfrac>\n            <mn>1<\/mn>\n            <mn>6<\/mn>\n          <\/mfrac>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mtext> \u0628\u0627 \u0627\u062d\u062a\u0645\u0627\u0644 <\/mtext>\n        <\/mtd>\n        <mtd>\n          <mfrac>\n            <mn>2<\/mn>\n            <mn>3<\/mn>\n          <\/mfrac>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mtext> \u0628\u0627 \u0627\u062d\u062a\u0645\u0627\u0644 <\/mtext>\n        <\/mtd>\n        <mtd>\n          <mfrac>\n            <mn>1<\/mn>\n            <mn>6<\/mn>\n          <\/mfrac>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p>\u0631\u0648\u0634 \u0628\u0627\u0644\u0627 \u0645\u0639\u0627\u062f\u0644 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u0639\u062f\u0627\u062f \u0627\u0632 \u0628\u06cc\u0646 \u0627\u0633\u062a <code>{+k,0,-k}<\/code> \u0645\u0633\u062a\u0642\u0631 \u0631\u0648\u06cc \u0646\u062a\u06cc\u062c\u0647 \u0627\u0646\u062f\u0627\u062e\u062a\u0646 \u06cc\u06a9 \u062a\u0627\u0633  \u0627\u06af\u0631 \u0627\u0645\u062a\u06cc\u0627\u0632 \u062a\u0627\u0633 \u0628\u0627\u0634\u062f <em>1<\/em>\u060c \u0633\u067e\u0633 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u062f <em>+k<\/em>.  \u0627\u06af\u0631 \u0627\u0645\u062a\u06cc\u0627\u0632 \u062a\u0627\u0633 \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647 \u0628\u0627\u0634\u062f <code>(2,5)<\/code>\u060c \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u062f <em>0<\/em>\u060c \u0648 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u062f <em>-k<\/em> \u0628\u0631\u0627\u06cc \u0646\u0645\u0631\u0647 \u062a\u0627\u0633 \u0627\u0632 <em>6<\/em>.<\/p>\n<p>\u06cc\u06a9 \u0631\u0648\u0634 \u06a9\u0644\u06cc \u062a\u0631 \u0627\u0632 a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f <code>density<\/code> \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0628\u0631\u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc.  \u0628\u0627 \u062a\u0646\u0638\u06cc\u0645 \\(s=\\frac{1}{\\text{density}}\\)\u060c \u0639\u0646\u0627\u0635\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 Random Projection \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u0634\u0648\u0646\u062f:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <msub>\n    <mi>\u0622\u0631<\/mi>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mi>\u0645\u0646<\/mi>\n      <mi>j<\/mi>\n    <\/mrow>\n  <\/msub>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>{<\/mo>\n    <mtable columnalign=\"left left\" rowspacing=\".2em\" columnspacing=\"1em\" displaystyle=\"false\">\n      <mtr>\n        <mtd>\n          <mo>+<\/mo>\n          <msqrt>\n            <mfrac>\n              <mi>\u0633<\/mi>\n              <mi>\u062f<\/mi>\n            <\/mfrac>\n          <\/msqrt>\n        <\/mtd>\n        <mtd>\n          <mtext> \u0628\u0627 \u0627\u062d\u062a\u0645\u0627\u0644 <\/mtext>\n        <\/mtd>\n        <mtd>\n          <mfrac>\n            <mn>1<\/mn>\n            <mrow>\n              <mn>2<\/mn>\n              <mi>\u0633<\/mi>\n            <\/mrow>\n          <\/mfrac>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mtext> \u0628\u0627 \u0627\u062d\u062a\u0645\u0627\u0644 <\/mtext>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n          <mo>&#8211;<\/mo>\n          <mfrac>\n            <mn>1<\/mn>\n            <mi>\u0633<\/mi>\n          <\/mfrac>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <msqrt>\n            <mfrac>\n              <mi>\u0633<\/mi>\n              <mi>\u062f<\/mi>\n            <\/mfrac>\n          <\/msqrt>\n        <\/mtd>\n        <mtd>\n          <mtext> \u0628\u0627 \u0627\u062d\u062a\u0645\u0627\u0644 <\/mtext>\n        <\/mtd>\n        <mtd>\n          <mfrac>\n            <mn>1<\/mn>\n            <mrow>\n              <mn>2<\/mn>\n              <mi>\u0633<\/mi>\n            <\/mrow>\n          <\/mfrac>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p>\u062a\u0648\u0635\u06cc\u0647 \u06a9\u0644\u06cc \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0646\u06cc\u062f <code>density<\/code> \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0628\u0647 \\(\\frac{1}{\\sqrt n}\\).<\/p>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0642\u0628\u0644\u0627 \u0630\u06a9\u0631 \u0634\u062f\u060c \u0628\u0631\u0627\u06cc \u0647\u0631 \u062f\u0648 \u0631\u0648\u0634 \u06af\u0627\u0648\u0633\u06cc \u0648 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u062a\u0639\u0627\u0645\u062f \u0648\u0627\u0642\u0639\u06cc \u0646\u06cc\u0633\u062a.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0641\u0636\u0627\u0647\u0627\u06cc \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u0628\u0627\u0644\u0627\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0634\u062f\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06cc\u06a9\u06cc \u0627\u0632 \u062f\u0648 \u0631\u0648\u0634 \u0641\u0648\u0642 <strong><em>\u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647<\/em><\/strong>  \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u062a\u0639\u0627\u0631\u0641<\/p>\n<h2 id=\"randomprojectionusingscikitlearn\"><span class=\"ez-toc-section\" id=\"%d8%b7%d8%b1%d8%ad_%d8%b1%db%8c%d8%b2%db%8c_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_scikit-learn\"><\/span>\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Scikit-Learn \u062f\u0631 \u0627\u062e\u062a\u06cc\u0627\u0631 \u0645\u0627 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u062f <code>random_projection<\/code> \u0645\u0627\u0698\u0648\u0644\u060c \u06a9\u0647 \u062f\u0627\u0631\u0627\u06cc \u0633\u0647 \u06a9\u0644\u0627\u0633 \/ \u0645\u0627\u0698\u0648\u0644 \u0645\u0647\u0645 \u0627\u0633\u062a:<\/p>\n<ul>\n<li><code>johnson_lindenstrauss_min_dim()<\/code>: \u0628\u0631\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u062d\u062f\u0627\u0642\u0644 \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f\u0647 \u0647\u0646\u06af\u0627\u0645 \u062f\u0627\u062f\u0647 \u0634\u062f\u0646 \u062d\u062c\u0645 \u0646\u0645\u0648\u0646\u0647 <code>m<\/code>.<\/li>\n<li><code>GaussianRandomProjection<\/code>: \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u062f.<\/li>\n<li><code>SparseRandomProjection<\/code>: \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u062f.<\/li>\n<\/ul>\n<p>\u0645\u0627 \u0647\u0631 \u0633\u0647 \u0645\u0648\u0631\u062f \u0641\u0648\u0642 \u0631\u0627 \u062f\u0631 \u0628\u062e\u0634 \u0647\u0627\u06cc \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f\u060c \u0627\u0645\u0627 \u0627\u0628\u062a\u062f\u0627 \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f import \u06a9\u0644\u0627\u0633 \u0647\u0627 \u0648 \u062a\u0648\u0627\u0628\u0639\u06cc \u06a9\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">from<\/span> sklearn.random_projection <span class=\"hljs-keyword\">import<\/span> SparseRandomProjection, johnson_lindenstrauss_min_dim\n<span class=\"hljs-keyword\">from<\/span> sklearn.random_projection <span class=\"hljs-keyword\">import<\/span> GaussianRandomProjection\n<span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n<span class=\"hljs-keyword\">from<\/span> matplotlib <span class=\"hljs-keyword\">import<\/span> pyplot <span class=\"hljs-keyword\">as<\/span> plt\n<span class=\"hljs-keyword\">import<\/span> sklearn.datasets <span class=\"hljs-keyword\">as<\/span> dt\n<span class=\"hljs-keyword\">from<\/span> sklearn.metrics.pairwise <span class=\"hljs-keyword\">import<\/span> euclidean_distances\n<\/code><\/pre>\n<h3 id=\"determiningtheminimumnumberofdimensionsviajohnsonlindenstrausslemma\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%b9%db%8c%db%8c%d9%86_%d8%ad%d8%af%d8%a7%d9%82%d9%84_%d8%aa%d8%b9%d8%af%d8%a7%d8%af_%d8%a7%d8%a8%d8%b9%d8%a7%d8%af_%d8%a7%d8%b2_%d8%b7%d8%b1%db%8c%d9%82_%d9%84%d9%85_%d8%ac%d8%a7%d9%86%d8%b3%d9%88%d9%86_%d9%84%db%8c%d9%86%d8%af%d9%86_%d8%a7%d8%b4%d8%aa%d8%b1%d8%a7%d9%88%d8%b3\"><\/span>\u062a\u0639\u06cc\u06cc\u0646 \u062d\u062f\u0627\u0642\u0644 \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0631\u0627 <code>johnson_lindenstrauss_min_dim()<\/code> \u062a\u0627\u0628\u0639 \u062d\u062f\u0627\u0642\u0644 \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u0631\u0627 \u062a\u0639\u06cc\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f <code>d<\/code>\u060c \u06a9\u0647 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u0646\u0645\u0648\u0646\u0647\u060c \u0645\u06cc \u062a\u0648\u0627\u0646 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0648\u0631\u0648\u062f\u06cc \u0631\u0627 \u0628\u0647 \u0622\u0646 \u0646\u06af\u0627\u0634\u062a <code>m<\/code>\u060c \u0648 <code>eps<\/code> \u06cc\u0627 \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \\(\\epsilon\\).<\/p>\n<p>\u06a9\u062f \u0632\u06cc\u0631 \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u0645\u062a\u0641\u0627\u0648\u062a\u06cc \u0627\u0632 \u0646\u0645\u0648\u0646\u0647\u200c\u0647\u0627 \u0622\u0632\u0645\u0627\u06cc\u0634 \u0645\u06cc\u200c\u06a9\u0646\u062f \u062a\u0627 \u062d\u062f\u0627\u0642\u0644 \u0627\u0646\u062f\u0627\u0632\u0647 \u0641\u0636\u0627\u06cc \u06a9\u0645\u200c\u0628\u0639\u062f \u0631\u0627 \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u062f\u060c \u06a9\u0647 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0645\u0634\u062e\u0635 \u0631\u0627 \u062d\u0641\u0638 \u0645\u06cc\u200c\u06a9\u0646\u062f. <strong><em>&#8220;\u0628\u06cc \u062e\u0637\u0631&#8221;<\/em><\/strong>  \u062a\u062d\u0631\u06cc\u0641 \u062f\u0627\u062f\u0647 \u0647\u0627<\/p>\n<p>\u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646\u060c \u0622\u0646 \u0631\u0627 \u062a\u0631\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f <code>log(d)<\/code> \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062e\u062a\u0644\u0641 <code>eps<\/code> \u0628\u0631\u0627\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0646\u0645\u0648\u0646\u0647 <code>m<\/code>.<\/p>\n<p>\u0646\u06a9\u062a\u0647 \u0645\u0647\u0645\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u0647 \u0622\u0646 \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646 \u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633 \u0627\u0646\u062f\u0627\u0632\u0647 \u0641\u0636\u0627\u06cc \u06a9\u0645\u200c\u0628\u0639\u062f \\(d\\) \u0631\u0627 \u0641\u0642\u0637 \u0628\u0631 \u0627\u0633\u0627\u0633 \u062a\u0639\u06cc\u06cc\u0646 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0631\u0648\u06cc \u062a\u0639\u062f\u0627\u062f \u0646\u0642\u0627\u0637 \u0645\u062b\u0627\u0644 \\(m\\) \u062f\u0631 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0648\u0631\u0648\u062f\u06cc.  \u062a\u0639\u062f\u0627\u062f \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627 \u06cc\u0627 \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627\u06cc \\(n\\) \u062f\u0627\u062f\u0647 \u0627\u0635\u0644\u06cc \u0646\u0627\u0645\u0631\u0628\u0648\u0637 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">eps = np.arange(<span class=\"hljs-number\">0.001<\/span>, <span class=\"hljs-number\">0.999<\/span>, <span class=\"hljs-number\">0.01<\/span>)\ncolors = (<span class=\"hljs-string\">'b'<\/span>, <span class=\"hljs-string\">'g'<\/span>, <span class=\"hljs-string\">'m'<\/span>, <span class=\"hljs-string\">'c'<\/span>)\nm = (<span class=\"hljs-number\">1e1<\/span>, <span class=\"hljs-number\">1e3<\/span>, <span class=\"hljs-number\">1e7<\/span>, <span class=\"hljs-number\">1e10<\/span>)\n<span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">4<\/span>):\n    min_dim = johnson_lindenstrauss_min_dim(n_samples=m(i), eps=eps)\n    label = <span class=\"hljs-string\">'Total samples = '<\/span> + <span class=\"hljs-built_in\">str<\/span>(m(i))\n    plt.plot(eps, np.log10(min_dim), c=colors(i), label=label)\n    \nplt.xlabel(<span class=\"hljs-string\">'eps'<\/span>)\nplt.ylabel(<span class=\"hljs-string\">'log$_{10}$(d)'<\/span>)\nplt.axhline(y=<span class=\"hljs-number\">3.5<\/span>, color=<span class=\"hljs-string\">'k'<\/span>, linestyle=<span class=\"hljs-string\">':'<\/span>)\nplt.legend()\nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-2.png\" alt=\"\u0646\u062d\u0648\u0647 \u062a\u0639\u06cc\u06cc\u0646 \u0627\u0646\u062f\u0627\u0632\u0647 \u0641\u0636\u0627\u06cc \u0627\u0628\u0639\u0627\u062f \u067e\u0627\u06cc\u06cc\u0646 \u062a\u0631 \u0628\u0631\u0627\u06cc \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc\" title=\"\"><\/p>\n<p>\u0627\u0632 \u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u0627\u0644\u0627\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u06a9\u0648\u0686\u06a9 \u0627\u0632 <code>eps<\/code>\u060c <code>d<\/code> \u0628\u0633\u06cc\u0627\u0631 \u0628\u0632\u0631\u06af \u0627\u0633\u062a \u0627\u0645\u0627 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f <code>eps<\/code> \u0628\u0647 \u06cc\u06a9\u06cc \u0646\u0632\u062f\u06cc\u06a9 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u0628\u0639\u0627\u062f \u0632\u06cc\u0631 3500 (\u062e\u0637 \u0633\u06cc\u0627\u0647 \u0646\u0642\u0637\u0647 \u0686\u06cc\u0646) \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062a\u0648\u0633\u0637 \u200b\u200b\u062a\u0627 \u0628\u0632\u0631\u06af \u0627\u0633\u062a <code>eps<\/code>.<\/p>\n<blockquote>\n<p>\u0627\u06cc\u0646 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u062f\u0631\u062e\u0648\u0627\u0633\u062a <strong>\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc<\/strong> \u0641\u0642\u0637 \u0645\u0639\u0646\u06cc \u062f\u0627\u0631\u0647 <strong>\u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u0628\u0627\u0644\u0627<\/strong>\u060c \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 \u0647\u0632\u0627\u0631\u0627\u0646 \u0648\u06cc\u0698\u06af\u06cc.  \u062f\u0631 \u0686\u0646\u06cc\u0646 \u0645\u0648\u0627\u0631\u062f\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u06a9\u0627\u0647\u0634 \u0632\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0627\u0628\u0639\u0627\u062f \u062f\u0633\u062a \u06cc\u0627\u0641\u062a.<\/p>\n<\/blockquote>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc\u200c\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0645\u062a\u0646 \u06cc\u0627 \u062a\u0635\u0648\u06cc\u0631\u060c \u06a9\u0647 \u0634\u0627\u0645\u0644 \u062a\u0639\u062f\u0627\u062f \u0632\u06cc\u0627\u062f\u06cc \u0648\u06cc\u0698\u06af\u06cc \u0648\u0631\u0648\u062f\u06cc \u0627\u0633\u062a\u060c \u0628\u0633\u06cc\u0627\u0631 \u0645\u0648\u0641\u0642 \u0647\u0633\u062a\u0646\u062f\u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0645\u0624\u0644\u0641\u0647 \u0627\u0635\u0644\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f<\/p>\n<h3 id=\"datatransformation\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%a8%d8%af%db%8c%d9%84_%d8%af%d8%a7%d8%af%d9%87_%d9%87%d8%a7\"><\/span>\u062a\u0628\u062f\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u067e\u0627\u06cc\u062a\u0648\u0646 \u0634\u0627\u0645\u0644 \u0627\u062c\u0631\u0627\u06cc \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc\u200c\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0648 \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc\u200c\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u062f\u0631 \u062e\u0648\u062f \u0645\u06cc\u200c\u0634\u0648\u062f. <code>sklearn<\/code> \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u062f\u0648 \u06a9\u0644\u0627\u0633 <code>GaussianRandomProjection<\/code> \u0648 <code>SparseRandomProjection<\/code> \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628.  \u0628\u0631\u062e\u06cc \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0645\u0647\u0645 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u0644\u0627\u0633 \u0647\u0627 \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632 (\u0644\u06cc\u0633\u062a \u06a9\u0627\u0645\u0644 \u0646\u06cc\u0633\u062a):<\/p>\n<ul>\n<li><code>n_components<\/code>: \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f\u0647.  \u0627\u06af\u0631 \u062a\u0646\u0638\u06cc\u0645 \u0634\u062f\u0647 \u0628\u0627\u0634\u062f <code>auto<\/code>\u060c \u0633\u067e\u0633 \u0627\u0628\u0639\u0627\u062f \u0628\u0647\u06cc\u0646\u0647 \u0642\u0628\u0644 \u0627\u0632 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u0645\u06cc \u0634\u0648\u062f<\/li>\n<li><code>eps<\/code>: \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633\u060c \u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u0631\u0627 \u06a9\u0646\u062a\u0631\u0644 \u0645\u06cc \u06a9\u0646\u062f \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647 \u0627\u0639\u0648\u062c\u0627\u062c \u062f\u0631 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0634\u062f\u0647 \u062f\u0631 \u06cc\u06a9 \u0645\u062d\u062f\u0648\u062f\u0647 \u0645\u0634\u062e\u0635 \u0646\u06af\u0647 \u062f\u0627\u0634\u062a\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/li>\n<li><code>density<\/code>: \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc <code>SparseRandomProjection<\/code>.  \u0645\u0642\u062f\u0627\u0631 \u067e\u06cc\u0634 \u0641\u0631\u0636 \u0627\u0633\u062a <code>auto<\/code>\u060c \u06a9\u0647 \\(s=\\frac{1}{\\sqrt n}\\) \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0646\u0638\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f.<\/li>\n<\/ul>\n<p>\u0645\u0627\u0646\u0646\u062f \u0633\u0627\u06cc\u0631 \u06a9\u0644\u0627\u0633 \u0647\u0627\u06cc \u06a9\u0627\u0647\u0634 \u0627\u0628\u0639\u0627\u062f <code>sklearn<\/code>\u060c \u0647\u0631 \u062f\u0648 \u0627\u06cc\u0646 \u06a9\u0644\u0627\u0633 \u0647\u0627 \u0634\u0627\u0645\u0644 \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f \u0647\u0633\u062a\u0646\u062f <code>fit()<\/code> \u0648 <code>fit_transform()<\/code> \u0645\u0648\u0627\u062f \u0648 \u0631\u0648\u0634 \u0647\u0627.  \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u06a9\u0647 \u0645\u0641\u06cc\u062f \u0647\u0633\u062a\u0646\u062f \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/p>\n<ul>\n<li><code>n_components<\/code>: \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u0641\u0636\u0627\u06cc \u062c\u062f\u06cc\u062f \u0631\u0648\u06cc \u06a9\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0645\u06cc \u0634\u0648\u062f.<\/li>\n<li><code>components_<\/code>: \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0628\u062f\u06cc\u0644 \u06cc\u0627 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc.<\/li>\n<li><code>density_<\/code>: \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc <code>SparseRandomProjection<\/code>.  \u0627\u0631\u0632\u0634 \u0622\u0646 \u0627\u0633\u062a <code>density<\/code> \u0645\u0633\u062a\u0642\u0631 \u0631\u0648\u06cc \u06a9\u0647 \u0639\u0646\u0627\u0635\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f.<\/li>\n<\/ul>\n<h4 id=\"randomprojectionwithgaussianrandomprojection\">\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0628\u0627 <em>\u067e\u0631\u0648\u062c\u06a9\u0634\u0646 \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc<\/em><\/h4>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627 <code>GaussianRandomProjection<\/code> \u06a9\u0644\u0627\u0633  \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a \u0647\u06cc\u0633\u062a\u0648\u06af\u0631\u0627\u0645 \u0631\u0633\u0645 \u0645\u06cc \u0634\u0648\u0646\u062f \u0648 \u0645\u06cc \u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0627\u0632 \u062a\u0648\u0632\u06cc\u0639 \u06af\u0627\u0648\u0633\u06cc \u0628\u0627 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0635\u0641\u0631 \u067e\u06cc\u0631\u0648\u06cc \u0645\u06cc \u06a9\u0646\u0646\u062f.  \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0627\u062f\u0647 \u0627\u0632 5000 \u0628\u0647 3947 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f:<\/p>\n<pre><code class=\"hljs\">X_rand = np.random.RandomState(<span class=\"hljs-number\">0<\/span>).rand(<span class=\"hljs-number\">100<\/span>, <span class=\"hljs-number\">5000<\/span>)\nproj_gauss = GaussianRandomProjection(random_state=<span class=\"hljs-number\">0<\/span>)\nX_transformed = proj_gauss.fit_transform(X_rand)\n\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Shape of transformed data: '<\/span> + <span class=\"hljs-built_in\">str<\/span>(X_transformed.shape))\n\n\nplt.hist(proj_gauss.components_.flatten())\nplt.title(<span class=\"hljs-string\">'Histogram of the flattened transformation matrix'<\/span>)\nplt.show()\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u06a9\u062f \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc \u062f\u0647\u062f:<\/p>\n<pre><code class=\"hljs\">Shape of transformed data: (100, 3947)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-3.png\" alt=\"\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc scikit-learn\" title=\"\"><\/p>\n<h4 id=\"randomprojectionwithsparserandomprojection\">\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0628\u0627 <em>SparseRandomProjection<\/em><\/h4>\n<p>\u06a9\u062f \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06cc\u06a9 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u062a\u0628\u062f\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f.  \u06a9\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0628\u062f\u06cc\u0644 \u0627\u0632 \u0633\u0647 \u0645\u0642\u062f\u0627\u0631 \u0645\u062c\u0632\u0627 \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0646\u0645\u0648\u062f\u0627\u0631 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0622\u0646\u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<p>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0628\u062f\u06cc\u0644 a \u0627\u0633\u062a <code>SciPy<\/code> \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 <code>csr_matrix<\/code>.  \u06a9\u062f \u0632\u06cc\u0631 \u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u063a\u06cc\u0631 \u0635\u0641\u0631 the \u062f\u0633\u062a\u0631\u0633\u06cc \u062f\u0627\u0631\u062f <code>csr_matrix<\/code> \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062f\u0631 \u0622\u0646 \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc \u06a9\u0646\u062f <code>p<\/code>.  \u0628\u0639\u062f\u060c \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f <code>p<\/code> \u0628\u0631\u0627\u06cc \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f\u0646 \u062a\u0639\u062f\u0627\u062f \u0639\u0646\u0627\u0635\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647:<\/p>\n<pre><code class=\"hljs\">proj_sparse = SparseRandomProjection(random_state=<span class=\"hljs-number\">0<\/span>)\nX_transformed = proj_sparse.fit_transform(X_rand)\n\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Shape of transformed data: '<\/span> + <span class=\"hljs-built_in\">str<\/span>(X_transformed.shape))\n\n\n\n\np = proj_sparse.components_.data\ntotal_elements = proj_sparse.components_.shape(<span class=\"hljs-number\">0<\/span>) *\\\n                  proj_sparse.components_.shape(<span class=\"hljs-number\">1<\/span>)\npos = p(p&gt;<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">0<\/span>)\nneg = p(p&lt;<span class=\"hljs-number\">0<\/span>)(<span class=\"hljs-number\">0<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Shape of transformation matrix: '<\/span>+ <span class=\"hljs-built_in\">str<\/span>(proj_sparse.components_.shape))\ncounts = (<span class=\"hljs-built_in\">sum<\/span>(p==neg), total_elements - <span class=\"hljs-built_in\">len<\/span>(p), <span class=\"hljs-built_in\">sum<\/span>(p==pos))\n\nplt.bar((neg, <span class=\"hljs-number\">0<\/span>, pos), counts, width=<span class=\"hljs-number\">0.1<\/span>)\nplt.xticks((neg, <span class=\"hljs-number\">0<\/span>, pos))\nplt.suptitle(<span class=\"hljs-string\">'Histogram of flattened transformation matrix, '<\/span> + \n             <span class=\"hljs-string\">'density = '<\/span> +\n             <span class=\"hljs-string\">'{:.2f}'<\/span>.<span class=\"hljs-built_in\">format<\/span>(proj_sparse.density_))\nplt.show()\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u062f\u0631:<\/p>\n<pre><code class=\"hljs\">Shape of transformed data: (100, 3947)\nShape of transformation matrix: (3947, 5000)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-4.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 scikit-learn\" title=\"\"><\/p>\n<p>\u0647\u06cc\u0633\u062a\u0648\u06af\u0631\u0627\u0645 \u0645\u0637\u0627\u0628\u0642 \u0628\u0627 \u0631\u0648\u0634 \u062a\u0648\u0644\u06cc\u062f \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0628\u062e\u0634 \u0642\u0628\u0644 \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a.  \u0635\u0641\u0631 \u0628\u0627 \u0627\u062d\u062a\u0645\u0627\u0644 (1-1\/100 = 0.99) \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u0634\u0648\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062d\u062f\u0648\u062f 99\u066a \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0635\u0641\u0631 \u0627\u0633\u062a.  \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0633\u0627\u062e\u062a\u0627\u0631\u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0648 \u0631\u0648\u0627\u0644 \u0628\u0631\u0627\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647\u060c \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062a\u0628\u062f\u06cc\u0644 \u0631\u0627 \u0628\u0633\u06cc\u0627\u0631 \u0633\u0631\u06cc\u0639 \u0648 \u06a9\u0627\u0631\u0622\u0645\u062f \u0645\u06cc \u06a9\u0646\u062f. \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af<\/p>\n<h2 id=\"practicalrandomprojectionswiththereuterscorpusvolume1dataset\"><span class=\"ez-toc-section\" id=\"%d9%be%db%8c%d8%b4_%d8%a8%db%8c%d9%86%db%8c_%d9%87%d8%a7%db%8c_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%d8%b9%d9%85%d9%84%db%8c_%d8%a8%d8%a7_%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87_%d8%ac%d9%84%d8%af_1_%d9%87%d8%b3%d8%aa%d9%87_%d8%b1%d9%88%db%8c%d8%aa%d8%b1%d8%b2\"><\/span>\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0639\u0645\u0644\u06cc \u0628\u0627 <em>\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062c\u0644\u062f 1 \u0647\u0633\u062a\u0647 \u0631\u0648\u06cc\u062a\u0631\u0632<\/em><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u06cc\u0646 \u0628\u062e\u0634 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u0631\u0648\u06cc \u0631\u0627 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.jmlr.org\/papers\/volume5\/lewis04a\/lewis04a.pdf\">\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062c\u0644\u062f \u0627\u0648\u0644 \u0631\u0648\u06cc\u062a\u0631\u0632<\/a>.  \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u0622\u0646\u0644\u0627\u06cc\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0631\u0627\u06cc\u06af\u0627\u0646 \u0642\u0627\u0628\u0644 \u062f\u0633\u062a\u0631\u0633\u06cc \u0627\u0633\u062a\u060c \u0627\u06af\u0631\u0686\u0647 \u0628\u0631\u0627\u06cc \u0627\u0647\u062f\u0627\u0641 \u0645\u0627\u060c \u0628\u0627\u0631\u06af\u06cc\u0631\u06cc \u0627\u0632 \u0637\u0631\u06cc\u0642 Scikit-Learn \u0622\u0633\u0627\u0646\u200c\u062a\u0631\u06cc\u0646 \u06a9\u0627\u0631 \u0627\u0633\u062a.<\/p>\n<p>\u0631\u0627 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/scikit-learn.org\/stable\/datasets\/real_world.html#rcv1-dataset\"><code>sklearn.datasets<\/code><\/a>  \u0645\u0627\u0698\u0648\u0644 \u0634\u0627\u0645\u0644 a <code>fetch_rcv1()<\/code> \u062a\u0627\u0628\u0639\u06cc \u06a9\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u062f\u0627\u0646\u0644\u0648\u062f \u0648 \u0648\u0627\u0631\u062f \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<div class=\"w-full\">\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u062f\u0627\u0646\u0644\u0648\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0686\u0646\u062f \u062f\u0642\u06cc\u0642\u0647 \u0637\u0648\u0644 \u0628\u06a9\u0634\u062f\u060c \u0627\u06af\u0631 \u0647\u0631\u06af\u0632 \u0622\u0646 \u0631\u0627 \u0627\u0632 \u0642\u0628\u0644 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0648\u0627\u0631\u062f \u0646\u06a9\u0631\u062f\u0647 \u0628\u0627\u0634\u06cc\u062f.  \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0646\u0648\u0627\u0631 \u067e\u06cc\u0634\u0631\u0641\u062a \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f\u060c \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0647 \u0646\u0638\u0631 \u0628\u0631\u0633\u062f \u06a9\u0647 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0628\u062f\u0648\u0646 \u067e\u06cc\u0634\u0631\u0641\u062a \u0628\u06cc\u0634\u062a\u0631 \u062f\u0631 \u062d\u0627\u0644 \u0622\u0648\u06cc\u0632\u0627\u0646 \u0627\u0633\u062a.  \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0622\u0646 \u0631\u0627 \u0627\u062c\u0631\u0627 \u0645\u06cc \u06a9\u0646\u06cc\u062f\u060c \u06a9\u0645\u06cc \u0628\u0647 \u0622\u0646 \u0632\u0645\u0627\u0646 \u0628\u062f\u0647\u06cc\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0686\u0646\u062f \u0628\u0631\u0686\u0633\u0628\u06cc \u0627\u0633\u062a\u060c \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0647\u0631 \u0646\u0642\u0637\u0647 \u062f\u0627\u062f\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0686\u0646\u062f\u06cc\u0646 \u06a9\u0644\u0627\u0633 \u0628\u0647 \u0637\u0648\u0631 \u0647\u0645\u0632\u0645\u0627\u0646 \u062a\u0639\u0644\u0642 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f \u0648 \u0627\u0632 103 \u06a9\u0644\u0627\u0633 \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a.  \u0647\u0631 \u0646\u0642\u0637\u0647 \u062f\u0627\u062f\u0647 \u062f\u0627\u0631\u0627\u06cc \u0627\u0628\u0639\u0627\u062f a \u0627\u0633\u062a <strong>\u0641\u0648\u0642 \u0627\u0644\u0639\u0627\u062f\u0647 47236<\/strong>\u060c \u0622\u0646 \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u0645\u0648\u0631\u062f \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0628\u0631\u0627\u06cc \u0627\u0639\u0645\u0627\u0644 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0633\u0631\u06cc\u0639 \u0648 \u0627\u0631\u0632\u0627\u0646 \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0646 \u0627\u062b\u0631\u0628\u062e\u0634\u06cc \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc\u200c\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc\u060c \u0648 \u0633\u0627\u062f\u0647 \u0646\u06af\u0647 \u062f\u0627\u0634\u062a\u0646 \u06a9\u0627\u0631\u0647\u0627\u060c 500 \u0646\u0642\u0637\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u062d\u062f\u0627\u0642\u0644 \u06cc\u06a9\u06cc \u0627\u0632 \u0633\u0647 \u06a9\u0644\u0627\u0633 \u0627\u0648\u0644 \u062a\u0639\u0644\u0642 \u062f\u0627\u0631\u0646\u062f.  \u0631\u0627 <code>fetch_rcv1()<\/code> \u062a\u0627\u0628\u0639 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u0628\u0627\u0632\u06cc\u0627\u0628\u06cc \u0645\u06cc \u06a9\u0646\u062f \u0648 \u06cc\u06a9 \u0634\u06cc \u0631\u0627 \u0628\u0627 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0648 \u0627\u0647\u062f\u0627\u0641\u06cc \u06a9\u0647 \u0647\u0631 \u062f\u0648 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0647\u0633\u062a\u0646\u062f \u0628\u0631\u0645\u06cc \u06af\u0631\u062f\u0627\u0646\u062f <code>CSR<\/code> \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0632 <code>SciPy<\/code>.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f Corpus \u0631\u0648\u06cc\u062a\u0631\u0632 \u0631\u0627 \u0648\u0627\u06a9\u0634\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0622\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0622\u0645\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">total_points = <span class=\"hljs-number\">500<\/span>\n\ndat = dt.fetch_rcv1()\n\ntarget_nz = dat.target.nonzero()\n\n\nind_class_123 = np.asarray(np.where((target_nz(<span class=\"hljs-number\">1<\/span>)==<span class=\"hljs-number\">0<\/span>) |\\\n                                    (target_nz(<span class=\"hljs-number\">1<\/span>)==<span class=\"hljs-number\">1<\/span>) |\\\n                                    (target_nz(<span class=\"hljs-number\">1<\/span>) == <span class=\"hljs-number\">2<\/span>))).flatten()\n\nnp.random.seed(<span class=\"hljs-number\">0<\/span>)\nind_class_123 = np.random.choice(ind_class_123, total_points, \n                                 replace=<span class=\"hljs-literal\">False<\/span>)\n\n\nrow_ind = target_nz(<span class=\"hljs-number\">0<\/span>)(ind_class_123)\nX = dat.data(row_ind,:)\ny = np.array(dat.target(row_ind,<span class=\"hljs-number\">0<\/span>:<span class=\"hljs-number\">3<\/span>).todense())\n<\/code><\/pre>\n<p>\u067e\u0633 \u0627\u0632 \u0622\u0645\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u060c \u0628\u0647 \u062a\u0627\u0628\u0639\u06cc \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u062a\u0635\u0648\u06cc\u0631\u06cc \u0627\u0632 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0634\u062f\u0647 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u062f.  \u0628\u0631\u0627\u06cc \u062f\u0627\u0634\u062a\u0646 \u0627\u06cc\u062f\u0647 \u0627\u06cc \u0627\u0632 \u06a9\u06cc\u0641\u06cc\u062a \u062a\u0628\u062f\u06cc\u0644\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0633\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0632\u06cc\u0631 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<ul>\n<li><code>dist_raw<\/code>: \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0648\u0627\u0635\u0644 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0632\u0648\u062c\u06cc \u0646\u0642\u0627\u0637 \u062f\u0627\u062f\u0647 \u0648\u0627\u0642\u0639\u06cc.<\/li>\n<li><code>dist_transform<\/code>: \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0648\u0627\u0635\u0644 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0632\u0648\u062c\u06cc \u0646\u0642\u0627\u0637 \u062f\u0627\u062f\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f\u0647.<\/li>\n<li><code>abs_diff<\/code>: \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0641\u0627\u0648\u062a \u0645\u0637\u0644\u0642 <code>dist_raw<\/code> \u0648 <code>dist_actual<\/code><\/li>\n<\/ul>\n<p>\u0631\u0627 <code>abs_diff_dist<\/code> \u0645\u0627\u062a\u0631\u06cc\u0633 \u0634\u0627\u062e\u0635 \u062e\u0648\u0628\u06cc \u0628\u0631\u0627\u06cc \u06a9\u06cc\u0641\u06cc\u062a \u062a\u0628\u062f\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0627\u0633\u062a.  \u0645\u0642\u0627\u062f\u06cc\u0631 \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u06cc\u0627 \u06a9\u0648\u0686\u06a9 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0627\u0639\u0648\u062c\u0627\u062c \u06a9\u0645 \u0648 \u062a\u0628\u062f\u06cc\u0644 \u062e\u0648\u0628 \u0627\u0633\u062a.  \u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u0633\u062a\u0642\u06cc\u0645\u0627\u064b \u062a\u0635\u0648\u06cc\u0631\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0647\u06cc\u0645 \u06cc\u0627 \u0647\u06cc\u0633\u062a\u0648\u06af\u0631\u0627\u0645 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0622\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0628\u0635\u0631\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645.  \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u062a\u0645\u0627\u0645 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u06cc\u06a9 \u0645\u0639\u06cc\u0627\u0631 \u06a9\u0645\u06cc \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645.<\/p>\n<p>\u06a9\u0627\u0631\u06a9\u0631\u062f <code>create_visualization()<\/code> \u0633\u0647 \u067e\u0644\u0627\u062a \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u062f.  \u0646\u0645\u0648\u062f\u0627\u0631 \u0627\u0648\u0644 \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0627\u0632 \u0646\u0642\u0627\u0637 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0634\u062f\u0647 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u062f\u0648 \u062c\u0647\u062a \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0648\u0644 \u0627\u0633\u062a.  \u0646\u0645\u0648\u062f\u0627\u0631 \u062f\u0648\u0645 \u062a\u0635\u0648\u06cc\u0631\u06cc \u0627\u0632 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0641\u0627\u0648\u062a \u0645\u0637\u0644\u0642 \u0648 \u0633\u0648\u0645\u06cc \u0647\u06cc\u0633\u062a\u0648\u06af\u0631\u0627\u0645 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0641\u0627\u0648\u062a \u0645\u0637\u0644\u0642 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">create_visualization<\/span>(<span class=\"hljs-params\">X_transform, y, abs_diff<\/span>):<\/span>\n    fig,ax = plt.subplots(nrows=<span class=\"hljs-number\">1<\/span>, ncols=<span class=\"hljs-number\">3<\/span>, figsize=(<span class=\"hljs-number\">20<\/span>,<span class=\"hljs-number\">7<\/span>))\n\n    plt.subplot(<span class=\"hljs-number\">131<\/span>)\n    plt.scatter(X_transform(y(:,<span class=\"hljs-number\">0<\/span>)==<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">0<\/span>), X_transform(y(:,<span class=\"hljs-number\">0<\/span>)==<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">1<\/span>), c=<span class=\"hljs-string\">'r'<\/span>, alpha=<span class=\"hljs-number\">0.4<\/span>)\n    plt.scatter(X_transform(y(:,<span class=\"hljs-number\">1<\/span>)==<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">0<\/span>), X_transform(y(:,<span class=\"hljs-number\">1<\/span>)==<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">1<\/span>), c=<span class=\"hljs-string\">'b'<\/span>, alpha=<span class=\"hljs-number\">0.4<\/span>)\n    plt.scatter(X_transform(y(:,<span class=\"hljs-number\">2<\/span>)==<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">0<\/span>), X_transform(y(:,<span class=\"hljs-number\">2<\/span>)==<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">1<\/span>), c=<span class=\"hljs-string\">'g'<\/span>, alpha=<span class=\"hljs-number\">0.4<\/span>)\n    plt.legend((<span class=\"hljs-string\">'Class 1'<\/span>, <span class=\"hljs-string\">'Class 2'<\/span>, <span class=\"hljs-string\">'Class 3'<\/span>))\n    plt.title(<span class=\"hljs-string\">'Projected data along first two dimensions'<\/span>)\n\n    plt.subplot(<span class=\"hljs-number\">132<\/span>)\n    plt.imshow(abs_diff)\n    plt.colorbar()\n    plt.title(<span class=\"hljs-string\">'Visualization of absolute differences'<\/span>)\n\n    plt.subplot(<span class=\"hljs-number\">133<\/span>)\n    ax = plt.hist(abs_diff.flatten())\n    plt.title(<span class=\"hljs-string\">'Histogram of absolute differences'<\/span>)\n\n    fig.subplots_adjust(wspace=<span class=\"hljs-number\">.3<\/span>) \n<\/code><\/pre>\n<h3 id=\"reutersdatasetgaussianrandomprojection\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87_%d8%b1%d9%88%db%8c%d8%aa%d8%b1%d8%b2_%d8%b7%d8%b1%d8%ad_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%da%af%d8%a7%d9%88%d8%b3%db%8c\"><\/span>\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0648\u06cc\u062a\u0631\u0632: \u0637\u0631\u062d \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0631\u0627 \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0648\u06cc\u062a\u0631\u0632 \u0627\u0639\u0645\u0627\u0644 \u06a9\u0646\u06cc\u0645.  \u06a9\u062f \u0632\u06cc\u0631 a \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f <code>for<\/code> \u062d\u0644\u0642\u0647 \u0628\u0631\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 <code>eps<\/code> \u0627\u0631\u0632\u0634 \u0647\u0627\u06cc.  \u0627\u06af\u0631 \u062d\u062f\u0627\u0642\u0644 \u0627\u0628\u0639\u0627\u062f \u0627\u06cc\u0645\u0646 \u062a\u0648\u0633\u0637 <code>johnson_lindenstrauss_min_dim<\/code> \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0627\u0628\u0639\u0627\u062f \u062f\u0627\u062f\u0647 \u0648\u0627\u0642\u0639\u06cc \u0627\u0633\u062a\u060c \u0633\u067e\u0633 \u0622\u0646 \u0631\u0627 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0645\u06cc \u06a9\u0646\u062f <code>fit_transform()<\/code> \u0631\u0648\u0634 \u0627\u0632 <code>GaussianRandomProjection<\/code>.  \u0631\u0627 <code>create_visualization()<\/code> \u0633\u067e\u0633 \u062a\u0627\u0628\u0639 \u0628\u0631\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u062a\u0635\u0648\u06cc\u0631\u0633\u0627\u0632\u06cc \u0628\u0631\u0627\u06cc \u0622\u0646 \u0645\u0642\u062f\u0627\u0631 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0645\u06cc \u0634\u0648\u062f <code>eps<\/code>.<\/p>\n<p>\u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631\u060c \u06a9\u062f \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0627\u062e\u062a\u0644\u0627\u0641 \u0645\u0637\u0644\u0642 \u0648 \u062f\u0631\u0635\u062f \u06a9\u0627\u0647\u0634 \u0627\u0628\u0639\u0627\u062f \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u062a\u0648\u0633\u0637 \u0637\u0631\u062d \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0631\u0627 \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n<pre><code class=\"hljs\">reduction_dim_gauss = ()\neps_arr_gauss = ()\nmean_abs_diff_gauss = ()\n<span class=\"hljs-keyword\">for<\/span> eps <span class=\"hljs-keyword\">in<\/span> np.arange(<span class=\"hljs-number\">0.1<\/span>, <span class=\"hljs-number\">0.999<\/span>, <span class=\"hljs-number\">0.2<\/span>):\n\n    min_dim = johnson_lindenstrauss_min_dim(n_samples=total_points, eps=eps)\n    <span class=\"hljs-keyword\">if<\/span> min_dim &gt; X.shape(<span class=\"hljs-number\">1<\/span>):\n        <span class=\"hljs-keyword\">continue<\/span>\n    gauss_proj = GaussianRandomProjection(random_state=<span class=\"hljs-number\">0<\/span>, eps=eps)\n    X_transform = gauss_proj.fit_transform(X)\n    dist_raw = euclidean_distances(X)\n    dist_transform = euclidean_distances(X_transform)\n    abs_diff_gauss = <span class=\"hljs-built_in\">abs<\/span>(dist_raw - dist_transform) \n\n    create_visualization(X_transform, y, abs_diff_gauss)\n    plt.suptitle(<span class=\"hljs-string\">'eps = '<\/span> + <span class=\"hljs-string\">'{:.2f}'<\/span>.<span class=\"hljs-built_in\">format<\/span>(eps) + <span class=\"hljs-string\">', n_components = '<\/span> + <span class=\"hljs-built_in\">str<\/span>(X_transform.shape(<span class=\"hljs-number\">1<\/span>)))\n    \n    reduction_dim_gauss.append(<span class=\"hljs-number\">100<\/span>-X_transform.shape(<span class=\"hljs-number\">1<\/span>)\/X.shape(<span class=\"hljs-number\">1<\/span>)*<span class=\"hljs-number\">100<\/span>)\n    eps_arr_gauss.append(eps)\n    mean_abs_diff_gauss.append(np.mean(abs_diff_gauss.flatten()))\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-5.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-6.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-7.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-8.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-9.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1\" title=\"\"><\/p>\n<p>\u062a\u0635\u0627\u0648\u06cc\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0641\u0627\u0648\u062a \u0645\u0637\u0644\u0642 \u0648 \u0647\u06cc\u0633\u062a\u0648\u06af\u0631\u0627\u0645 \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0622\u0646 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0627\u06a9\u062b\u0631 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u0647\u0633\u062a\u0646\u062f.  \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u060c \u0627\u06a9\u062b\u0631\u06cc\u062a \u0628\u0632\u0631\u06af\u06cc \u0627\u0632 \u062c\u0641\u062a \u0646\u0642\u0627\u0637 \u0641\u0627\u0635\u0644\u0647 \u0648\u0627\u0642\u0639\u06cc \u062e\u0648\u062f \u0631\u0627 \u062f\u0631 \u0641\u0636\u0627\u06cc \u06a9\u0645 \u0627\u0628\u0639\u0627\u062f \u062d\u0641\u0638 \u0645\u06cc \u06a9\u0646\u0646\u062f \u0648 \u0633\u0627\u062e\u062a\u0627\u0631 \u0627\u0635\u0644\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u062d\u0641\u0638 \u0645\u06cc \u06a9\u0646\u0646\u062f.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u06a9\u06cc\u0641\u06cc\u062a \u062f\u06af\u0631\u06af\u0648\u0646\u06cc\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u062a\u0641\u0627\u0648\u062a \u0645\u0637\u0644\u0642 \u0631\u0627 \u062f\u0631 \u0645\u0642\u0627\u0628\u0644 \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645 <code>eps<\/code>.  \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0647\u0631 \u0686\u0647 \u0627\u0631\u0632\u0634 \u0628\u0627\u0644\u0627\u062a\u0631 \u0628\u0627\u0634\u062f <code>eps<\/code>\u060c \u06a9\u0627\u0647\u0634 \u0627\u0628\u0639\u0627\u062f \u0628\u06cc\u0634\u062a\u0631 \u0627\u0633\u062a.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u062f\u0631\u0635\u062f \u06a9\u0627\u0647\u0634 \u062f\u0631 \u0645\u0642\u0627\u0628\u0644 \u0631\u0627 \u0646\u06cc\u0632 \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645. <code>eps<\/code> \u062f\u0631 \u0637\u0631\u062d \u0641\u0631\u0639\u06cc \u062f\u0648\u0645:<\/p>\n<pre><code class=\"hljs\">fig,ax = plt.subplots(nrows=<span class=\"hljs-number\">1<\/span>, ncols=<span class=\"hljs-number\">2<\/span>, figsize=(<span class=\"hljs-number\">10<\/span>,<span class=\"hljs-number\">5<\/span>))\nplt.subplot(<span class=\"hljs-number\">121<\/span>)\nplt.plot(eps_arr_gauss, mean_abs_diff_gauss, marker=<span class=\"hljs-string\">'o'<\/span>, c=<span class=\"hljs-string\">'g'<\/span>)\nplt.xlabel(<span class=\"hljs-string\">'eps'<\/span>)\nplt.ylabel(<span class=\"hljs-string\">'Mean absolute difference'<\/span>)\n\nplt.subplot(<span class=\"hljs-number\">122<\/span>)\nplt.plot(eps_arr_gauss, reduction_dim_gauss, marker = <span class=\"hljs-string\">'o'<\/span>, c=<span class=\"hljs-string\">'m'<\/span>)\nplt.xlabel(<span class=\"hljs-string\">'eps'<\/span>)\nplt.ylabel(<span class=\"hljs-string\">'Percentage reduction in dimensionality'<\/span>)\n\nfig.subplots_adjust(wspace=<span class=\"hljs-number\">.4<\/span>) \nplt.suptitle(<span class=\"hljs-string\">'Assessing the Quality of Gaussian Random Projections'<\/span>)\nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-10.png\" alt=\"\u06a9\u06cc\u0641\u06cc\u062a \u06a9\u0627\u0647\u0634 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc RCV1\" title=\"\"><\/p>\n<p>\u0645\u06cc \u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0637\u0631\u062d \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0628\u0639\u0627\u062f \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u06a9\u0627\u0647\u0634 \u062f\u0647\u06cc\u0645 <strong>\u0628\u06cc\u0634 \u0627\u0632 99%<\/strong>!  \u0627\u06af\u0631\u0686\u0647\u060c \u0627\u06cc\u0646 <em>\u0645\u06cc\u06a9\u0646\u062f<\/em> \u0628\u0647 \u0642\u06cc\u0645\u062a \u062a\u062d\u0631\u06cc\u0641 \u0628\u06cc\u0634\u062a\u0631 \u062f\u0627\u062f\u0647 \u0647\u0627 \u062a\u0645\u0627\u0645 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<h3 id=\"reutersdatasetsparserandomprojection\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87_%d8%b1%d9%88%db%8c%d8%aa%d8%b1%d8%b2_%d8%b7%d8%b1%d8%ad_%d8%b1%db%8c%d8%b2%db%8c_%d8%aa%d8%b5%d8%a7%d8%af%d9%81%db%8c_%d9%be%d8%b1%d8%a7%da%a9%d9%86%d8%af%d9%87\"><\/span>\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0648\u06cc\u062a\u0631\u0632: \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u0634\u0627\u0628\u0647\u06cc \u0631\u0627 \u0628\u0627 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">reduction_dim_sparse = ()\neps_arr_sparse = ()\nmean_abs_diff_sparse = ()\n<span class=\"hljs-keyword\">for<\/span> eps <span class=\"hljs-keyword\">in<\/span> np.arange(<span class=\"hljs-number\">0.1<\/span>, <span class=\"hljs-number\">0.999<\/span>, <span class=\"hljs-number\">0.2<\/span>):\n\n    min_dim = johnson_lindenstrauss_min_dim(n_samples=total_points, eps=eps)\n    <span class=\"hljs-keyword\">if<\/span> min_dim &gt; X.shape(<span class=\"hljs-number\">1<\/span>):\n        <span class=\"hljs-keyword\">continue<\/span>\n    sparse_proj = SparseRandomProjection(random_state=<span class=\"hljs-number\">0<\/span>, eps=eps, dense_output=<span class=\"hljs-number\">1<\/span>)\n    X_transform = sparse_proj.fit_transform(X)\n    dist_raw = euclidean_distances(X)\n    dist_transform = euclidean_distances(X_transform)\n    abs_diff_sparse = <span class=\"hljs-built_in\">abs<\/span>(dist_raw - dist_transform) \n\n    create_visualization(X_transform, y, abs_diff_sparse)\n    plt.suptitle(<span class=\"hljs-string\">'eps = '<\/span> + <span class=\"hljs-string\">'{:.2f}'<\/span>.<span class=\"hljs-built_in\">format<\/span>(eps) + <span class=\"hljs-string\">', n_components = '<\/span> + <span class=\"hljs-built_in\">str<\/span>(X_transform.shape(<span class=\"hljs-number\">1<\/span>)))\n    \n    reduction_dim_sparse.append(<span class=\"hljs-number\">100<\/span>-X_transform.shape(<span class=\"hljs-number\">1<\/span>)\/X.shape(<span class=\"hljs-number\">1<\/span>)*<span class=\"hljs-number\">100<\/span>)\n    eps_arr_sparse.append(eps)\n    mean_abs_diff_sparse.append(np.mean(abs_diff_sparse.flatten()))\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-11.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-12.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-13.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-14.png\" alt=\"\u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 RCV1\" title=\"\"><\/p>\n<p>\u062f\u0631 \u0645\u0648\u0631\u062f \u067e\u0631\u0648\u062c\u06a9\u0634\u0646 \u062a\u0635\u0627\u062f\u0641\u06cc\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0641\u0627\u0648\u062a \u0645\u0637\u0644\u0642 \u0634\u0628\u06cc\u0647 \u0628\u0647 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u06af\u0627\u0648\u0633\u06cc \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f.  \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0634\u062f\u0647 \u0631\u0648\u06cc \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u062f\u0648 \u0628\u0639\u062f \u0627\u0648\u0644 \u062f\u0627\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u06cc \u062c\u0627\u0644\u0628 \u062a\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0646\u0642\u0627\u0637 \u0632\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0622\u0646 \u062a\u0631\u0633\u06cc\u0645 \u0634\u062f\u0647 \u0627\u0633\u062a \u0631\u0648\u06cc \u0645\u062d\u0648\u0631 \u0645\u062e\u062a\u0635\u0627\u062a<\/p>\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0627\u062e\u062a\u0644\u0627\u0641 \u0645\u0637\u0644\u0642 \u0648 \u062f\u0631\u0635\u062f \u06a9\u0627\u0647\u0634 \u0627\u0628\u0639\u0627\u062f \u0631\u0627 \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062e\u062a\u0644\u0641 \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645 <code>eps<\/code> \u067e\u0627\u0631\u0627\u0645\u062a\u0631:<\/p>\n<pre><code class=\"hljs\">fig,ax = plt.subplots(nrows=<span class=\"hljs-number\">1<\/span>, ncols=<span class=\"hljs-number\">2<\/span>, figsize=(<span class=\"hljs-number\">10<\/span>,<span class=\"hljs-number\">5<\/span>))\nplt.subplot(<span class=\"hljs-number\">121<\/span>)\nplt.plot(eps_arr_sparse, mean_abs_diff_sparse, marker=<span class=\"hljs-string\">'o'<\/span>, c=<span class=\"hljs-string\">'g'<\/span>)\nplt.xlabel(<span class=\"hljs-string\">'eps'<\/span>)\nplt.ylabel(<span class=\"hljs-string\">'Mean absolute difference'<\/span>)\n\nplt.subplot(<span class=\"hljs-number\">122<\/span>)\nplt.plot(eps_arr_sparse, reduction_dim_sparse, marker = <span class=\"hljs-string\">'o'<\/span>, c=<span class=\"hljs-string\">'m'<\/span>)\nplt.xlabel(<span class=\"hljs-string\">'eps'<\/span>)\nplt.ylabel(<span class=\"hljs-string\">'Percentage reduction in dimensionality'<\/span>)\n\nfig.subplots_adjust(wspace=<span class=\"hljs-number\">.4<\/span>) \nplt.suptitle(<span class=\"hljs-string\">'Assessing the Quality of Sparse Random Projections'<\/span>)\nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/random-projection-theory-and-implementation-in-python-with-scikit-learn-15.png\" alt=\"\u06a9\u06cc\u0641\u06cc\u062a \u06a9\u0627\u0647\u0634 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0631\u0627\u06a9\u0646\u062f\u0647\" title=\"\"><\/p>\n<p>\u0631\u0648\u0646\u062f \u062f\u0648 \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u0634\u0627\u0628\u0647 \u0631\u0648\u0646\u062f \u06cc\u06a9 \u0637\u0631\u062d \u06af\u0627\u0648\u0633\u06cc \u0627\u0633\u062a.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u062a\u0641\u0627\u0648\u062a \u0645\u0637\u0644\u0642 \u0628\u0631\u0627\u06cc \u0637\u0631\u062d \u06af\u0627\u0648\u0633\u06cc \u06a9\u0645\u062a\u0631 \u0627\u0632 \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0633\u062a.<\/p>\n<h2 id=\"conclusions\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87_%da%af%db%8c%d8%b1%db%8c\"><\/span>\u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627\u060c \u062c\u0632\u0626\u06cc\u0627\u062a \u062f\u0648 \u0646\u0648\u0639 \u0627\u0635\u0644\u06cc \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc\u060c \u06cc\u0639\u0646\u06cc \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u06af\u0627\u0648\u0633\u06cc \u0648 \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0631\u0627 \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u06cc\u0645.<\/p>\n<p>\u0645\u0627 \u062c\u0632\u0626\u06cc\u0627\u062a \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u06a9\u0631\u062f\u06cc\u0645 <strong><em>\u0644\u0645 \u062c\u0627\u0646\u0633\u0648\u0646-\u0644\u06cc\u0646\u062f\u0646 \u0627\u0634\u062a\u0631\u0627\u0648\u0633<\/em><\/strong>\u060c \u0645\u0628\u0646\u0627\u06cc \u0631\u06cc\u0627\u0636\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0647\u0627 \u0627\u0633\u062a.  \u0633\u067e\u0633 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f <code>sklearn<\/code> \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647<\/p>\n<p>\u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0627\u06cc\u0646 \u062f\u0648 \u0631\u0648\u0634 \u0631\u0627 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u06cc\u0645 \u0631\u0648\u06cc \u06cc\u06a9 \u0632\u0646\u062f\u06af\u06cc \u0648\u0627\u0642\u0639\u06cc <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.jmlr.org\/papers\/volume5\/lewis04a\/lewis04a.pdf\">\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062c\u0644\u062f \u0627\u0648\u0644 \u0631\u0648\u06cc\u062a\u0631\u0632<\/a>.<\/p>\n<p>\u0645\u0627 \u062e\u0648\u0627\u0646\u0646\u062f\u0647 \u0631\u0627 \u062a\u0634\u0648\u06cc\u0642 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0631\u0627 \u062f\u0631 \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u0646\u0638\u0627\u0631\u062a \u0634\u062f\u0647 \u06cc\u0627 \u0648\u0638\u0627\u06cc\u0641 \u0631\u06af\u0631\u0633\u06cc\u0648\u0646 \u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u067e\u06cc\u0634\u200c\u067e\u0631\u062f\u0627\u0632\u0634\u060c \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0628\u0639\u062f\u06cc \u0633\u0631\u0648\u06a9\u0627\u0631 \u062f\u0627\u0631\u062f\u060c \u0627\u0645\u062a\u062d\u0627\u0646 \u06a9\u0646\u062f.<\/p>\n<\/div>\n<p><script>\n                        !function(f,b,e,v,n,t,s)\n                        {if(f.fbq)return;n=f.fbq=function(){n.callMethod?\n                        n.callMethod.apply(n,arguments):n.queue.push(arguments)};\n                        if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';\n                        n.queue=();t=b.createElement(e);t.async=!0;\n                        t.src=v;s=b.getElementsByTagName(e)(0);\n                        s.parentNode.insertBefore(t,s)}(window, document,'script',\n                        'https:\/\/connect.facebook.net\/en_US\/fbevents.js');\n                        fbq('init', '525232124909042');\n                        fbq('track', 'PageView');\n                    <\/script>    (\u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627 \u0628\u0647 \u062a\u0631\u062c\u0645\u0647)# python<br \/>\n<br \/><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1403-01-09 00:02:02<br \/>\n<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;15124&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;0&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;0&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628&quot;,&quot;legend&quot;:&quot;0\\\/5 (0 \u0631\u0627\u06cc)&quot;,&quot;size&quot;:&quot;30&quot;,&quot;title&quot;:&quot;\u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc: \u062a\u0626\u0648\u0631\u06cc \u0648 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0628\u0627 Scikit-Learn&quot;,&quot;width&quot;:&quot;0&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} ({count} \u0631\u0627\u06cc)&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 0px;\">\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 24px;\">\n            <span class=\"kksr-muted\">\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628<\/span>\n    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 11<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627 \u0645\u0642\u062f\u0645\u0647\u200c\u0627\u06cc \u0639\u0645\u06cc\u0642 \u0628\u0631\u0627\u06cc \u062a\u06a9\u0646\u06cc\u06a9 \u06a9\u0627\u0647\u0634 \u0627\u0628\u0639\u0627\u062f \u0628\u062f\u0648\u0646 \u0646\u0638\u0627\u0631\u062a \u0627\u0633\u062a \u06a9\u0647 \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc. \u06cc\u06a9 \u0637\u0631\u062d \u0631\u06cc\u0632\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0631\u0627\u06cc \u06a9\u0627\u0647\u0634 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0648 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f \u0648 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0622\u0633\u0627\u0646 \u062a\u0631 \u06a9\u0646\u062f process \u0648 \u062a\u062c\u0633\u0645 \u06a9\u0646\u06cc\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u06cc\u06a9 \u062a\u06a9\u0646\u06cc\u06a9 \u067e\u06cc\u0634 \u067e\u0631\u062f\u0627\u0632\u0634 \u0628\u0631\u0627\u06cc \u0622\u0645\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0648\u0631\u0648\u062f\u06cc \u0628\u0647 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":15125,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[],"class_list":["post-15124","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","category-programming"],"acf":[],"_links":{"self":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/15124","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/comments?post=15124"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/15124\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/15125"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=15124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=15124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=15124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}