{"id":14319,"date":"2024-01-04T20:05:56","date_gmt":"2024-01-04T16:35:56","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/"},"modified":"2024-01-04T20:05:56","modified_gmt":"2024-01-04T16:35:56","slug":"%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/","title":{"rendered":"\u0631\u0627\u0647\u0646\u0645\u0627\u06cc \u0642\u0637\u0639\u06cc \u0628\u0631\u0627\u06cc K-Means Clustering \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%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%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%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d8%a7%d9%86%da%af%db%8c%d8%b2%d9%87\" >\u0627\u0646\u06af\u06cc\u0632\u0647<\/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%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d8%b1%d9%88%d8%b4_%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_%d8%af%d8%b3%d8%aa%db%8c_%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85_k-means\" >\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062f\u0633\u062a\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means<\/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%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d9%87%d9%85%d9%87_%d8%a7%db%8c%d9%86%d9%87%d8%a7_%da%86%d9%87_%d8%b1%d8%a8%d8%b7%db%8c_%d8%a8%d9%87_%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85_k-means_%d8%af%d8%a7%d8%b1%d8%af%d8%9f\" >\u0647\u0645\u0647 \u0627\u06cc\u0646\u0647\u0627 \u0686\u0647 \u0631\u0628\u0637\u06cc \u0628\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u062f\u0627\u0631\u062f\u061f<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d8%b1%d9%88%d8%b4_%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85_k-means_%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_scikit-learn\" >\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn<\/a><\/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%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d8%b1%d9%88%d8%b4_%d8%a2%d8%b1%d9%86%d8%ac_%e2%80%93_%d8%a7%d9%86%d8%aa%d8%ae%d8%a7%d8%a8_%d8%a8%d9%87%d8%aa%d8%b1%db%8c%d9%86_%d8%aa%d8%b9%d8%af%d8%a7%d8%af_%da%af%d8%b1%d9%88%d9%87\" >\u0631\u0648\u0634 \u0622\u0631\u0646\u062c &#8211; \u0627\u0646\u062a\u062e\u0627\u0628 \u0628\u0647\u062a\u0631\u06cc\u0646 \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0648\u0647<\/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%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87_%d8%af%d8%b3%d8%aa%db%8c_%d8%af%d8%b1%d9%88%d9%86_%d9%85%d8%ac%d9%85%d9%88%d8%b9_%d9%85%d8%b1%d8%a8%d8%b9%e2%80%8c%d9%87%d8%a7_wcss\" >\u0645\u062d\u0627\u0633\u0628\u0647 \u062f\u0633\u062a\u06cc \u062f\u0631\u0648\u0646 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u200c\u0647\u0627 (WCSS)<\/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%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d8%af%d8%b1_%d8%ad%d8%a7%d9%84_%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87_wcss_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%da%a9%d8%b1%d8%af%d9%86_scikit-learn\" >\u062f\u0631 \u062d\u0627\u0644 \u0645\u062d\u0627\u0633\u0628\u0647 WCSS \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f\u0646 Scikit-Learn<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d9%85%d8%b9%db%8c%d8%a7%d8%b1%d9%87%d8%a7%db%8c_%da%a9%db%8c%d9%81%db%8c_%d8%ae%d9%88%d8%b4%d9%87_%d8%a7%db%8c_%d8%ac%d8%a7%db%8c%da%af%d8%b2%db%8c%d9%86\" >\u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u06a9\u06cc\u0641\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_k-means_%d8%b1%d9%88%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_%d8%af%db%8c%da%af%d8%b1\" >\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 K-Means \u0631\u0648\u06cc \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062f\u06cc\u06af\u0631<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%b1%d8%a7%d9%87%d9%86%d9%85%d8%a7%db%8c-%d9%82%d8%b7%d8%b9%db%8c-%d8%a8%d8%b1%d8%a7%db%8c-k-means-clustering-%d8%a8%d8%a7-scikit-learn\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87\" >\u0646\u062a\u06cc\u062c\u0647<\/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\"> 17<\/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><em>K-\u0628\u0647 \u0645\u0639\u0646\u06cc \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0627\u0633\u062a<\/em> \u06cc\u06a9\u06cc \u0627\u0632 \u067e\u0631\u06a9\u0627\u0631\u0628\u0631\u062f\u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646\u06cc \u0628\u062f\u0648\u0646 \u0646\u0638\u0627\u0631\u062a \u0627\u0633\u062a \u06a9\u0647 \u062e\u0648\u0634\u0647\u200c\u0647\u0627\u06cc\u06cc \u0627\u0632 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0631\u0627 \u062a\u0634\u06a9\u06cc\u0644 \u0645\u06cc\u200c\u062f\u0647\u062f. \u0631\u0648\u06cc \u0634\u0628\u0627\u0647\u062a \u0628\u06cc\u0646 \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u062f\u0627\u062f\u0647<\/p>\n<blockquote>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627\u060c \u0627\u0628\u062a\u062f\u0627 \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0633\u0627\u062f\u0647 \u0645\u06cc \u0627\u0646\u062f\u0627\u0632\u06cc\u0645 \u062a\u0627 \u0628\u0641\u0647\u0645\u06cc\u0645 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f \u0642\u0628\u0644 \u0627\u0632 \u0627\u062c\u0631\u0627\u06cc \u0622\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn.  \u0633\u067e\u0633\u060c \u0631\u0648\u0634 \u062a\u0639\u06cc\u06cc\u0646 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627 (Ks) \u062f\u0631 K-Means \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u0641\u0627\u0635\u0644\u0647\u060c \u0648\u0627\u0631\u06cc\u0627\u0646\u0633\u060c \u0648 \u0645\u0632\u0627\u06cc\u0627 \u0648 \u0645\u0639\u0627\u06cc\u0628 K-Means \u0631\u0627 \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f.<\/p>\n<\/blockquote>\n<h2 id=\"motivation\"><span class=\"ez-toc-section\" id=\"%d8%a7%d9%86%da%af%db%8c%d8%b2%d9%87\"><\/span>\u0627\u0646\u06af\u06cc\u0632\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0648\u0636\u0639\u06cc\u062a \u0632\u06cc\u0631 \u0631\u0627 \u062a\u0635\u0648\u0631 \u06a9\u0646\u06cc\u062f.  \u06cc\u06a9 \u0631\u0648\u0632\u060c \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u062f\u0631 \u0627\u0637\u0631\u0627\u0641 \u0645\u062d\u0644\u0647 \u0642\u062f\u0645 \u0645\u06cc \u0632\u062f\u06cc\u062f\u060c \u0645\u062a\u0648\u062c\u0647 \u0634\u062f\u06cc\u062f \u06a9\u0647 10 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0631\u0641\u0627\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u0648 \u0634\u0631\u0648\u0639 \u0628\u0647 \u062a\u0639\u062c\u0628 \u06a9\u0631\u062f\u06cc\u062f \u06a9\u0647 \u06a9\u062f\u0627\u0645 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0647\u0627 \u0634\u0628\u06cc\u0647 \u0628\u0647 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0647\u0633\u062a\u0646\u062f &#8211; \u062f\u0631 \u0645\u062c\u0627\u0648\u0631\u062a \u06cc\u06a9\u062f\u06cc\u06af\u0631.  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u0631\u0627\u0647 \u0647\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u067e\u0627\u0633\u062e \u0628\u0647 \u0627\u06cc\u0646 \u0633\u0648\u0627\u0644 \u0647\u0633\u062a\u06cc\u062f\u060c \u0628\u0627 \u0631\u0648\u06cc\u06a9\u0631\u062f \u062c\u0627\u0644\u0628\u06cc \u0628\u0631\u062e\u0648\u0631\u062f \u06a9\u0631\u062f\u0647 \u0627\u06cc\u062f \u06a9\u0647 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0647 \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f. \u0631\u0648\u06cc \u0645\u062e\u062a\u0635\u0627\u062a \u0622\u0646\u0647\u0627 \u0631\u0648\u06cc \u0646\u0642\u0634\u0647.<\/p>\n<p>\u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0627\u06af\u0631 \u06cc\u06a9 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u062f\u0631 5 \u06a9\u06cc\u0644\u0648\u0645\u062a\u0631\u06cc \u063a\u0631\u0628 \u0648 3 \u06a9\u06cc\u0644\u0648\u0645\u062a\u0631\u06cc \u0634\u0645\u0627\u0644 \u0642\u0631\u0627\u0631 \u062f\u0627\u0634\u062a &#8211; \u0634\u0645\u0627 \u0622\u0646 \u0631\u0627 \u0627\u062e\u062a\u0635\u0627\u0635 \u0645\u06cc \u062f\u0647\u06cc\u062f <code>(5, 3)<\/code> \u0645\u062e\u062a\u0635\u0627\u062a \u0622\u0646 \u0627\u0633\u062a \u0648 \u0622\u0646 \u0631\u0627 \u062f\u0631 \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u06cc\u0646 \u0627\u0648\u0644\u06cc\u0646 \u0646\u0642\u0637\u0647 \u0631\u0627 \u062a\u0631\u0633\u06cc\u0645 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0622\u0646\u0686\u0647 \u0631\u0627 \u06a9\u0647 \u0627\u062a\u0641\u0627\u0642 \u0645\u06cc\u200c\u0627\u0641\u062a\u062f \u062a\u062c\u0633\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> matplotlib.pyplot <span class=\"hljs-keyword\">as<\/span> plt\n\nplt.title(<span class=\"hljs-string\">\"Store With Coordinates (5, 3)\"<\/span>)\nplt.scatter(x=<span class=\"hljs-number\">5<\/span>, y=<span class=\"hljs-number\">3<\/span>)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-1.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0627\u06cc\u0646 \u0641\u0642\u0637 \u0627\u0648\u0644\u06cc\u0646 \u0646\u06a9\u062a\u0647 \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u06cc\u062f\u0647 \u0627\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f \u0631\u0648\u0634 \u0646\u0645\u0627\u06cc\u0646\u062f\u06af\u06cc \u06cc\u06a9 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645.  \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0645\u0627 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 10 \u0645\u062e\u062a\u0635\u0627\u062a \u0628\u0631\u0627\u06cc 10 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u062c\u0645\u0639 \u0622\u0648\u0631\u06cc \u0634\u062f\u0647 \u062f\u0627\u0631\u06cc\u0645.  \u067e\u0633 \u0627\u0632 \u0633\u0627\u0632\u0645\u0627\u0646\u062f\u0647\u06cc \u0622\u0646\u0647\u0627 \u062f\u0631 \u06cc\u06a9 <code>numpy<\/code> \u0622\u0631\u0627\u06cc\u0647\u060c \u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u06a9\u0627\u0646 \u0647\u0627\u06cc \u0622\u0646\u0647\u0627 \u0631\u0627 \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n\npoints = np.array(((<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">3<\/span>), (<span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">15<\/span>), (<span class=\"hljs-number\">15<\/span>, <span class=\"hljs-number\">12<\/span>), (<span class=\"hljs-number\">24<\/span>, <span class=\"hljs-number\">10<\/span>), (<span class=\"hljs-number\">30<\/span>, <span class=\"hljs-number\">45<\/span>), (<span class=\"hljs-number\">85<\/span>, <span class=\"hljs-number\">70<\/span>), (<span class=\"hljs-number\">71<\/span>, <span class=\"hljs-number\">80<\/span>), (<span class=\"hljs-number\">60<\/span>, <span class=\"hljs-number\">78<\/span>), (<span class=\"hljs-number\">55<\/span>, <span class=\"hljs-number\">52<\/span>),(<span class=\"hljs-number\">80<\/span>, <span class=\"hljs-number\">91<\/span>)))\n\nxs = points(:,<span class=\"hljs-number\">0<\/span>) \nys = points(:,<span class=\"hljs-number\">1<\/span>)  \n\nplt.title(<span class=\"hljs-string\">\"10 Stores Coordinates\"<\/span>)\nplt.scatter(x=xs, y=ys)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-2.png\" alt=\"\" title=\"\"><\/p>\n<h2 id=\"howtomanuallyimplementkmeansalgorithm\"><span class=\"ez-toc-section\" id=\"%d8%b1%d9%88%d8%b4_%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_%d8%af%d8%b3%d8%aa%db%8c_%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85_k-means\"><\/span>\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062f\u0633\u062a\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0647 10 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631\u060c \u0648 \u0645\u0634\u06a9\u0644 \u0627\u0635\u0644\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0631\u0627\u0647\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0647 \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f \u0631\u0648\u06cc \u0646\u0632\u062f\u06cc\u06a9\u06cc\u061f  \u0641\u0642\u0637 \u0628\u0627 \u0646\u06af\u0627\u0647\u06cc \u06af\u0630\u0631\u0627 \u0628\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u060c \u0627\u062d\u062a\u0645\u0627\u0644\u0627 \u0645\u062a\u0648\u062c\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u0634\u062f <em>\u062f\u0648 \u06af\u0631\u0648\u0647 \u0641\u0631\u0648\u0634\u06af\u0627\u0647<\/em> &#8211; \u06cc\u06a9\u06cc \u0646\u0642\u0627\u0637 \u067e\u0627\u06cc\u06cc\u0646 \u0628\u0647 \u0633\u0645\u062a \u0686\u067e-\u067e\u0627\u06cc\u06cc\u0646 \u0648 \u062f\u06cc\u06af\u0631\u06cc \u0646\u0642\u0627\u0637 \u0628\u0627\u0644\u0627-\u0631\u0627\u0633\u062a \u0627\u0633\u062a.  \u0634\u0627\u06cc\u062f \u062d\u062a\u06cc \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0646 \u062f\u0648 \u0646\u0642\u0637\u0647 \u0631\u0627 \u062f\u0631 \u0648\u0633\u0637 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u06af\u0631\u0648\u0647 \u0645\u062c\u0632\u0627 \u0627\u0632 \u0647\u0645 \u0645\u062a\u0645\u0627\u06cc\u0632 \u06a9\u0646\u06cc\u0645 &#8211; \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u06cc\u062c\u0627\u062f <em>\u0633\u0647 \u06af\u0631\u0648\u0647 \u0645\u062e\u062a\u0644\u0641<\/em>.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0628\u062e\u0634 \u0628\u0647 \u0628\u0631\u0631\u0633\u06cc \u0622\u0646 \u062e\u0648\u0627\u0647\u06cc\u0645 \u067e\u0631\u062f\u0627\u062e\u062a process \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u062f\u0633\u062a\u06cc \u0646\u0642\u0627\u0637 &#8211; \u062a\u0642\u0633\u06cc\u0645 \u0622\u0646\u0647\u0627 \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u0645\u0639\u06cc\u0646 \u06af\u0631\u0648\u0647.  \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628\u060c \u0645\u0627 \u0627\u0633\u0627\u0633\u0627\u064b \u062a\u0645\u0627\u0645 \u0645\u0631\u0627\u062d\u0644 \u0631\u0627 \u0628\u0627 \u062f\u0642\u062a \u0645\u0631\u0648\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <strong>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc K-Means<\/strong>.  \u062f\u0631 \u067e\u0627\u06cc\u0627\u0646 \u0627\u06cc\u0646 \u0628\u062e\u0634\u060c \u062f\u0631\u06a9 \u0628\u0635\u0631\u06cc \u0648 \u0639\u0645\u0644\u06cc \u0627\u0632 \u062a\u0645\u0627\u0645 \u0645\u0631\u0627\u062d\u0644 \u0627\u0646\u062c\u0627\u0645 \u0634\u062f\u0647 \u062f\u0631 \u0637\u0648\u0644 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc K-Means \u0628\u0647 \u062f\u0633\u062a \u062e\u0648\u0627\u0647\u06cc\u062f \u0622\u0648\u0631\u062f.  \u067e\u0633 \u0627\u0632 \u0622\u0646\u060c \u0622\u0646 \u0631\u0627 \u0628\u0647 Scikit-Learn \u0648\u0627\u06af\u0630\u0627\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0628\u0647\u062a\u0631\u06cc\u0646 \u0631\u0627\u0647 \u0628\u0631\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u0648\u062c\u0648\u062f \u062f\u0648 \u06cc\u0627 \u0633\u0647 \u06af\u0631\u0648\u0647 \u0627\u0632 \u0646\u0642\u0627\u0637 \u0686\u06cc\u0633\u062a\u061f  \u06cc\u06a9 \u0631\u0627\u0647 \u0633\u0627\u062f\u0647 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u06cc\u06a9 \u062a\u0639\u062f\u0627\u062f\u06cc \u0627\u0632 \u06af\u0631\u0648\u0647 \u0647\u0627 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u062f &#8211; \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u062f\u0648 &#8211; \u0648 \u0633\u067e\u0633 \u0633\u0639\u06cc \u06a9\u0646\u06cc\u062f \u0646\u0642\u0627\u0637 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u06af\u0631\u0648\u0647 \u0628\u0646\u062f\u06cc \u06a9\u0646\u06cc\u062f \u0631\u0648\u06cc \u0622\u0646 \u0627\u0646\u062a\u062e\u0627\u0628<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-3.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u06af\u0648\u06cc\u06cc\u0645 \u06a9\u0647 \u0645\u0627 \u062a\u0635\u0645\u06cc\u0645 \u06af\u0631\u0641\u062a\u0647 \u0627\u06cc\u0645 \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f <em>\u062f\u0648 \u06af\u0631\u0648\u0647<\/em> \u0627\u0632 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0647\u0627\u06cc \u0645\u0627 (\u0646\u0642\u0627\u0637).  \u062d\u0627\u0644 \u0628\u0627\u06cc\u062f \u0631\u0627\u0647\u06cc \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0641\u0647\u0645\u06cc\u0645 \u06a9\u062f\u0627\u0645 \u0646\u0642\u0627\u0637 \u0628\u0647 \u06a9\u062f\u0627\u0645 \u06af\u0631\u0648\u0647 \u062a\u0639\u0644\u0642 \u062f\u0627\u0631\u0646\u062f.  \u0627\u06cc\u0646 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0628\u0631\u0627\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0646 \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f <em>\u06af\u0631\u0648\u0647 1<\/em> \u0648 \u06cc\u06a9\u06cc \u0628\u0631\u0627\u06cc \u0646\u0645\u0627\u06cc\u0646\u062f\u06af\u06cc <em>\u06af\u0631\u0648\u0647 2<\/em>.  \u0627\u06cc\u0646 \u0646\u0642\u0627\u0637 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u0631\u062c\u0639 \u062f\u0631 \u0647\u0646\u06af\u0627\u0645 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u062f\u06cc\u06af\u0631 \u0628\u0647 \u0647\u0631 \u06af\u0631\u0648\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>\u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628\u060c \u0646\u06a9\u062a\u0647 \u0631\u0627 \u0628\u06af\u0648\u06cc\u06cc\u062f <code>(5, 3)<\/code> \u0628\u0647 \u06af\u0631\u0648\u0647 1 \u062a\u0639\u0644\u0642 \u0645\u06cc \u06af\u06cc\u0631\u062f \u0648 \u0627\u0645\u062a\u06cc\u0627\u0632 \u0645\u06cc \u06af\u06cc\u0631\u062f <code>(79, 60)<\/code> \u0628\u0647 \u06af\u0631\u0648\u0647 2. \u0647\u0646\u06af\u0627\u0645 \u062a\u0644\u0627\u0634 \u0628\u0631\u0627\u06cc \u0627\u062e\u062a\u0635\u0627\u0635 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u062c\u062f\u06cc\u062f <code>(6, 3)<\/code> \u0628\u0647 \u06af\u0631\u0648\u0647 \u0647\u0627\u060c \u0628\u0627\u06cc\u062f \u0641\u0627\u0635\u0644\u0647 \u0622\u0646 \u0631\u0627 \u062a\u0627 \u0622\u0646 \u062f\u0648 \u0646\u0642\u0637\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u06a9\u0646\u06cc\u0645.  \u062f\u0631 \u0645\u0648\u0631\u062f \u0646\u0642\u0637\u0647 <code>(6, 3)<\/code> \u0627\u0633\u062a <em>\u0646\u0632\u062f\u06cc\u06a9 \u062a\u0631<\/em> \u0628\u0647 <code>(5, 3)<\/code>\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u062a\u0639\u0644\u0642 \u0628\u0647 \u06af\u0631\u0648\u0647\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062a\u0648\u0633\u0637 \u0622\u0646 \u0646\u0642\u0637\u0647 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a &#8211; <em>\u06af\u0631\u0648\u0647 1<\/em>.  \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u0631\u0627 \u062f\u0631 \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637\u0647 \u06af\u0631\u0648\u0647 \u0628\u0646\u062f\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<blockquote>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644\u060c \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u062a\u0639\u06cc\u06cc\u0646 \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0648\u0647 \u0647\u0627 (<em>\u062e\u0648\u0634\u0647 \u0647\u0627<\/em>) &#8211; \u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u062f\u0631 \u062d\u0627\u0644 \u0627\u0646\u062a\u062e\u0627\u0628 \u0628\u0631\u062e\u06cc \u0627\u0632 \u0646\u0642\u0627\u0637 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 a <em>\u0627\u0631\u062c\u0627\u0639<\/em> \u0641\u0627\u0635\u0644\u0647 \u0627\u0645\u062a\u06cc\u0627\u0632\u0627\u062a \u062c\u062f\u06cc\u062f \u0647\u0631 \u06af\u0631\u0648\u0647<\/p>\n<\/blockquote>\n<p>\u0627\u06cc\u0646 \u0627\u06cc\u062f\u0647 \u06a9\u0644\u06cc \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0634\u0628\u0627\u0647\u062a \u0647\u0627\u06cc \u0628\u06cc\u0646 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0647\u0627\u06cc \u0645\u0627 \u0627\u0633\u062a.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0622\u0646 \u0631\u0627 \u0639\u0645\u0644\u06cc \u06a9\u0646\u06cc\u0645 &#8211; \u0627\u0628\u062a\u062f\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062f\u0648 \u0646\u0642\u0637\u0647 \u0645\u0631\u062c\u0639 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u0645 <em>\u062a\u0635\u0627\u062f\u0641\u06cc<\/em>.  \u0646\u0642\u0637\u0647 \u0645\u0631\u062c\u0639 \u0627\u0632 <em>\u06af\u0631\u0648\u0647 1<\/em> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f <code>(5, 3)<\/code> \u0648 \u0646\u0642\u0637\u0647 \u0645\u0631\u062c\u0639 \u0627\u0632 <em>\u06af\u0631\u0648\u0647 2<\/em> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f <code>(10, 15)<\/code>.  \u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0647\u0631 \u062f\u0648 \u0646\u0642\u0637\u0647 \u062e\u0648\u062f \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u0645 <code>numpy<\/code> \u0622\u0631\u0627\u06cc\u0647 \u062a\u0648\u0633\u0637 <code>(0)<\/code> \u0648 <code>(1)<\/code> \u0627\u06cc\u0646\u062f\u06a9\u0633 \u0647\u0627 \u0648 \u0630\u062e\u06cc\u0631\u0647 \u0622\u0646\u0647\u0627 \u062f\u0631 <code>g1<\/code> (\u06af\u0631\u0648\u0647 1) \u0648 <code>g2<\/code> \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc (\u06af\u0631\u0648\u0647 2):<\/p>\n<pre><code class=\"hljs\">g1 = points(<span class=\"hljs-number\">0<\/span>)\ng2 = points(<span class=\"hljs-number\">1<\/span>)\n<\/code><\/pre>\n<p>\u067e\u0633 \u0627\u0632 \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631\u060c \u0628\u0627\u06cc\u062f \u0641\u0627\u0635\u0644\u0647 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u062f\u06cc\u06af\u0631 \u062a\u0627 \u0622\u0646 \u0646\u0642\u0627\u0637 \u0645\u0631\u062c\u0639 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645.  \u0627\u06cc\u0646 \u06cc\u06a9 \u0633\u0648\u0627\u0644 \u0645\u0647\u0645 \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u062f &#8211; \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0622\u0646 \u0641\u0627\u0635\u0644\u0647 \u0631\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u06a9\u0631\u062f.  \u0627\u0633\u0627\u0633\u0627\u064b \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0647\u0631 \u0627\u0646\u062f\u0627\u0632\u0647\u200c\u06af\u06cc\u0631\u06cc \u0641\u0627\u0635\u0644\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645\u060c \u0627\u0645\u0627 \u0628\u0631\u0627\u06cc \u0647\u062f\u0641 \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627\u060c \u0627\u0632 Euclidean Distance_ \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u062f\u0627\u0646\u0633\u062a\u0646 \u0627\u06cc\u0646\u06a9\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0641\u0627\u0635\u0644\u0647 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0645\u0628\u062a\u0646\u06cc \u0627\u0633\u062a \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0645\u0641\u06cc\u062f \u0628\u0627\u0634\u062f \u0631\u0648\u06cc \u0642\u0636\u06cc\u0647 \u0641\u06cc\u062b\u0627\u063a\u0648\u0631\u062b:<\/p>\n<p>$$<br \/>c^2 = a^2 + b^2<br \/>$$<\/p>\n<p>\u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0628\u0627 \u0646\u0642\u0627\u0637 \u06cc\u06a9 \u0647\u0648\u0627\u067e\u06cc\u0645\u0627 \u0633\u0627\u0632\u06af\u0627\u0631 \u0627\u0633\u062a &#8211; <code>(a1, b1)<\/code> \u0648 <code>(a2, b2)<\/code>\u060c \u0641\u0631\u0645\u0648\u0644 \u0642\u0628\u0644\u06cc \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<p>$$<br \/>c^2 = (a2-a1)^2 + (b2-b1)^2<br \/>$$<\/p>\n<p>\u0641\u0627\u0635\u0644\u0647 \u0645\u0631\u0628\u0639 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f root \u0627\u0632 <code>c<\/code>\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0641\u0631\u0645\u0648\u0644 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0628\u0646\u0648\u06cc\u0633\u06cc\u0645:<\/p>\n<p>$$<br \/>\u0627\u0642\u0644\u06cc\u062f\u0633\u06cc_{dist} = \\sqrt(2)((a2 &#8211; a1)^2 + (b2 &#8211; b1) ^2))<br \/>$$<\/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> \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0641\u0631\u0645\u0648\u0644 \u0641\u0627\u0635\u0644\u0647 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0646\u0642\u0627\u0637 \u0686\u0646\u062f \u0628\u0639\u062f\u06cc \u062a\u0639\u0645\u06cc\u0645 \u062f\u0647\u06cc\u062f.  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u062f\u0631 \u06cc\u06a9 \u0641\u0636\u0627\u06cc \u0633\u0647 \u0628\u0639\u062f\u06cc\u060c \u0646\u0642\u0627\u0637 \u062f\u0627\u0631\u0627\u06cc \u0633\u0647 \u0645\u062e\u062a\u0635\u0627\u062a \u0647\u0633\u062a\u0646\u062f &#8211; \u0641\u0631\u0645\u0648\u0644 \u0645\u0627 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0631\u0648\u0634 \u0632\u06cc\u0631 \u0645\u0646\u0639\u06a9\u0633 \u0645\u06cc \u06a9\u0646\u062f:<br \/>$$<br \/>\u0627\u0642\u0644\u06cc\u062f\u0633\u06cc_{dist} = \\sqrt(2)((a2 &#8211; a1)^2 + (b2 &#8211; b1) ^2 + (c2 &#8211; c1) ^2))<br \/>$$<br \/>\u0628\u062f\u0648\u0646 \u062a\u0648\u062c\u0647 \u0628\u0647 \u062a\u0639\u062f\u0627\u062f \u0627\u0628\u0639\u0627\u062f \u0641\u0636\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0645\u0634\u063a\u0648\u0644 \u0628\u0647 \u0641\u0639\u0627\u0644\u06cc\u062a \u0647\u0633\u062a\u06cc\u0645\u060c \u0627\u0632 \u0647\u0645\u06cc\u0646 \u0627\u0635\u0644 \u067e\u06cc\u0631\u0648\u06cc \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u062a\u0627 \u0627\u06cc\u0646\u062c\u0627 \u0645\u0627 \u0646\u0642\u0627\u0637\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0646\u0645\u0627\u06cc\u0634 \u06af\u0631\u0648\u0647 \u0647\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 \u0648 \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0641\u0627\u0635\u0644\u0647 \u0647\u0627 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645.  \u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0641\u0627\u0635\u0644\u0647 \u0647\u0627 \u0648 \u06af\u0631\u0648\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0627 \u062a\u062e\u0635\u06cc\u0635 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0627\u0645\u062a\u06cc\u0627\u0632\u0647\u0627\u06cc \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u062c\u0645\u0639 \u0622\u0648\u0631\u06cc \u0634\u062f\u0647 \u0628\u0647 \u06cc\u06a9 \u06af\u0631\u0648\u0647 \u06a9\u0646\u0627\u0631 \u0647\u0645 \u0642\u0631\u0627\u0631 \u062f\u0647\u06cc\u0645.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u062a\u062c\u0633\u0645 \u0628\u0647\u062a\u0631 \u0622\u0646\u060c \u0633\u0647 \u0644\u06cc\u0633\u062a \u0631\u0627 \u0627\u0639\u0644\u0627\u0645 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0627\u0648\u0644\u06cc\u0646 \u0646\u0641\u0631\u06cc \u06a9\u0647 \u0627\u0645\u062a\u06cc\u0627\u0632\u0647\u0627\u06cc \u06af\u0631\u0648\u0647 \u0627\u0648\u0644 \u0631\u0627 \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc \u06a9\u0646\u062f &#8211; <code>points_in_g1<\/code>.  \u0646\u0641\u0631 \u062f\u0648\u0645 \u0628\u0631\u0627\u06cc \u0630\u062e\u06cc\u0631\u0647 \u0627\u0645\u062a\u06cc\u0627\u0632 \u0627\u0632 \u06af\u0631\u0648\u0647 2 &#8211; <code>points_in_g2<\/code>\u0648 \u0622\u062e\u0631\u06cc\u0646 \u0645\u0648\u0631\u062f &#8211; <code>group<\/code>\u060c \u0628\u0647 <em>\u0628\u0631\u0686\u0633\u0628<\/em> \u0646\u0642\u0627\u0637 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0647\u0631 \u062f\u0648 <code>1<\/code> (\u0628\u0647 \u06af\u0631\u0648\u0647 1 \u062a\u0639\u0644\u0642 \u062f\u0627\u0631\u062f) \u06cc\u0627 <code>2<\/code> (\u0645\u062a\u0639\u0644\u0642 \u0628\u0647 \u06af\u0631\u0648\u0647 2)<\/p>\n<pre><code class=\"hljs\">points_in_g1 = ()\npoints_in_g2 = ()\ngroup = ()\n<\/code><\/pre>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0646\u0642\u0627\u0637 \u062e\u0648\u062f \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u06a9\u0646\u06cc\u0645 \u0648 \u0641\u0627\u0635\u0644\u0647 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0628\u06cc\u0646 \u0622\u0646\u0647\u0627 \u0648 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0645\u0631\u0627\u062c\u0639 \u06af\u0631\u0648\u0647 \u062e\u0648\u062f \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645.  \u0647\u0631 \u0646\u0642\u0637\u0647 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f <em>\u0646\u0632\u062f\u06cc\u06a9 \u062a\u0631<\/em> \u0628\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u062f\u0648 \u06af\u0631\u0648\u0647 &#8211; \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u0631\u0648\u06cc \u06a9\u062f\u0627\u0645 \u06af\u0631\u0648\u0647 \u0646\u0632\u062f\u06cc\u06a9\u200c\u062a\u0631\u06cc\u0646 \u0627\u0633\u062a\u060c \u0647\u0631 \u0646\u0642\u0637\u0647 \u0631\u0627 \u0628\u0647 \u0644\u06cc\u0633\u062a \u0645\u0631\u0628\u0648\u0637\u0647 \u0627\u062e\u062a\u0635\u0627\u0635 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 \u0648 \u062f\u0631 \u0639\u06cc\u0646 \u062d\u0627\u0644 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 <code>1<\/code> \u06cc\u0627 <code>2<\/code> \u0628\u0647 <code>group<\/code> \u0644\u06cc\u0633\u062a:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">for<\/span> p <span class=\"hljs-keyword\">in<\/span> points:\n    x1, y1 = p(<span class=\"hljs-number\">0<\/span>), p(<span class=\"hljs-number\">1<\/span>)\n    euclidean_distance_g1 = np.sqrt((g1(<span class=\"hljs-number\">0<\/span>) - x1)**<span class=\"hljs-number\">2<\/span> + (g1(<span class=\"hljs-number\">1<\/span>) - y1)**<span class=\"hljs-number\">2<\/span>)\n    euclidean_distance_g2 = np.sqrt((g2(<span class=\"hljs-number\">0<\/span>) - x1)**<span class=\"hljs-number\">2<\/span> + (g2(<span class=\"hljs-number\">1<\/span>) - y1)**<span class=\"hljs-number\">2<\/span>)\n    <span class=\"hljs-keyword\">if<\/span> euclidean_distance_g1 &lt; euclidean_distance_g2:\n        points_in_g1.append(p)\n        group.append(<span class=\"hljs-string\">'1'<\/span>)\n    <span class=\"hljs-keyword\">else<\/span>:\n        points_in_g2.append(p)\n        group.append(<span class=\"hljs-string\">'2'<\/span>)\n<\/code><\/pre>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u0646\u062a\u0627\u06cc\u062c \u0627\u06cc\u0646 \u062a\u06a9\u0631\u0627\u0631 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0686\u0647 \u0627\u062a\u0641\u0627\u0642\u06cc \u0627\u0641\u062a\u0627\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">f'points_in_g1:<span class=\"hljs-subst\">{points_in_g1}<\/span>\\n \\\n\\npoints_in_g2:<span class=\"hljs-subst\">{points_in_g2}<\/span>\\n \\\n\\ngroup:<span class=\"hljs-subst\">{group}<\/span>'<\/span>)\n<\/code><\/pre>\n<p>\u06a9\u0647 \u0645\u0646\u062c\u0631 \u0628\u0647:<\/p>\n<pre><code class=\"hljs\">points_in_g1:(array((5, 3)))\n \npoints_in_g2:(array((10, 15)), array((15, 12)), \n              array((24, 10)), array((30, 45)), \n              array((85, 70)), array((71, 80)),\n              array((60, 78)), array((55, 52)), \n              array((80, 91)))\n \ngroup:(1, 2, 2, 2, 2, 2, 2, 2, 2, 2) \n<\/code><\/pre>\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0646\u062a\u06cc\u062c\u0647 \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0631\u0627 \u0628\u0627 \u0631\u0646\u06af\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062a\u0631\u0633\u06cc\u0645 \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc \u0627\u062e\u062a\u0635\u0627\u0635 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Seaborn&#8217;s  <code>scatterplot()<\/code> \u0628\u0627 <code>group<\/code> \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 <code>hue<\/code> \u0628\u062d\u062b \u0648 \u062c\u062f\u0644:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> seaborn <span class=\"hljs-keyword\">as<\/span> sns\n\nsns.scatterplot(x=points(:, <span class=\"hljs-number\">0<\/span>), y=points(:, <span class=\"hljs-number\">1<\/span>), hue=group)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-4.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0628\u0647 \u0648\u0636\u0648\u062d \u0642\u0627\u0628\u0644 \u0645\u0634\u0627\u0647\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u062a\u0646\u0647\u0627 \u0646\u0642\u0637\u0647 \u0627\u0648\u0644 \u0645\u0627 \u0628\u0647 \u06af\u0631\u0648\u0647 1 \u0627\u062e\u062a\u0635\u0627\u0635 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a\u060c \u0648 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u062f\u06cc\u06af\u0631 \u0628\u0647 \u06af\u0631\u0648\u0647 2 \u0627\u062e\u062a\u0635\u0627\u0635 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u0628\u0627 \u0622\u0646\u0686\u0647 \u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u062a\u0635\u0648\u0631 \u0645\u06cc \u06a9\u0631\u062f\u06cc\u0645 \u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0633\u062a.  \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u062a\u0641\u0627\u0648\u062a \u0628\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0648 \u0627\u0646\u062a\u0638\u0627\u0631\u0627\u062a \u0627\u0648\u0644\u06cc\u0647 \u0645\u0627 &#8211; \u0622\u06cc\u0627 \u0631\u0627\u0647\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0646 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u06cc\u0645\u061f  \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f!<\/p>\n<p>\u06cc\u06a9 \u0631\u0648\u06cc\u06a9\u0631\u062f \u062a\u06a9\u0631\u0627\u0631 process \u0648 \u0646\u0642\u0627\u0637 \u0645\u062e\u062a\u0644\u0641 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u0631\u062c\u0639 \u06af\u0631\u0648\u0647 \u0647\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u062f.  \u0627\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0645\u0627 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u062f\u060c \u0627\u0645\u06cc\u062f\u0648\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0628\u06cc\u0634\u062a\u0631 \u0645\u0637\u0627\u0628\u0642 \u0628\u0627 \u0622\u0646\u0686\u0647 \u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u062a\u0635\u0648\u0631 \u0645\u06cc \u06a9\u0631\u062f\u06cc\u0645\u060c \u0628\u0627\u0634\u062f.  \u0627\u06cc\u0646 \u0628\u0627\u0631 \u062f\u0648\u0645\u060c \u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0646\u200c\u0647\u0627 \u0631\u0627 \u0646\u0647 \u0628\u0647\u200c\u0637\u0648\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u0627\u0646\u0646\u062f \u06af\u0630\u0634\u062a\u0647\u060c \u0628\u0644\u06a9\u0647 \u0628\u0627 \u06af\u0631\u0641\u062a\u0646 \u06cc\u06a9 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u0645 <em>\u0645\u0646\u0638\u0648\u0631 \u062f\u0627\u0634\u062a\u0646<\/em> \u0627\u0632 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u0627\u0632 \u0642\u0628\u0644 \u06af\u0631\u0648\u0647 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647 \u0645\u0627.  \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628\u060c \u0622\u0646 \u0646\u0642\u0627\u0637 \u062c\u062f\u06cc\u062f \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u062f\u0631 \u0648\u0633\u0637 \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637\u0647 \u0642\u0631\u0627\u0631 \u06af\u06cc\u0631\u0646\u062f.<\/p>\n<p>\u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0627\u06af\u0631 \u06af\u0631\u0648\u0647 \u062f\u0648\u0645 \u0641\u0642\u0637 \u0627\u0645\u062a\u06cc\u0627\u0632 \u062f\u0627\u0634\u062a <code>(10, 15)<\/code>\u060c <code>(30, 45)<\/code>.  \u062c\u062f\u06cc\u062f <em>\u0645\u0631\u06a9\u0632\u06cc<\/em> \u0646\u0642\u0637\u0647 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f <code>(10 + 30)\/2<\/code> \u0648 <code>(15+45)\/2<\/code> &#8211; \u06a9\u0647 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627 <code>(20, 30)<\/code>.<\/p>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u0627 \u0646\u062a\u0627\u06cc\u062c \u062e\u0648\u062f \u0631\u0627 \u062f\u0631 \u0644\u06cc\u0633\u062a \u0647\u0627 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0647 \u0627\u06cc\u0645\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0628\u062a\u062f\u0627 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0647 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0646\u06cc\u0645 <code>numpy<\/code> \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u060c xs\u060c ys \u0622\u0646\u0647\u0627 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u0647 \u0648 \u0633\u067e\u0633 \u0622\u0646 \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u062f <em>\u0645\u0646\u0638\u0648\u0631 \u062f\u0627\u0634\u062a\u0646<\/em>:<\/p>\n<pre><code class=\"hljs\">g1_center = (np.array(points_in_g1)(:, <span class=\"hljs-number\">0<\/span>).mean(), np.array(points_in_g1)(:, <span class=\"hljs-number\">1<\/span>).mean())\ng2_center = (np.array(points_in_g2)(:, <span class=\"hljs-number\">0<\/span>).mean(), np.array(points_in_g2)(:, <span class=\"hljs-number\">1<\/span>).mean())\ng1_center, g2_center\n<\/code><\/pre>\n<div class=\"alert alert-warn\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<div class=\"w-full\">\n<p><strong>\u0645\u0634\u0627\u0648\u0631\u0647:<\/strong> \u0633\u0639\u06cc \u06a9\u0646\u06cc\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f <code>numpy<\/code> \u0648 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc NumPy \u062a\u0627 \u062d\u062f \u0627\u0645\u06a9\u0627\u0646.  \u0622\u0646\u0647\u0627 \u0628\u0631\u0627\u06cc \u0639\u0645\u0644\u06a9\u0631\u062f \u0628\u0647\u062a\u0631 \u0628\u0647\u06cc\u0646\u0647 \u0634\u062f\u0647 \u0627\u0646\u062f \u0648 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0639\u0645\u0644\u06cc\u0627\u062a \u062c\u0628\u0631 \u062e\u0637\u06cc \u0631\u0627 \u0633\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u0646\u062f.  \u0647\u0631 \u0632\u0645\u0627\u0646 \u06a9\u0647 \u0633\u0639\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u062f \u0628\u0631\u062e\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u062c\u0628\u0631 \u062e\u0637\u06cc \u0631\u0627 \u062d\u0644 \u06a9\u0646\u06cc\u062f\u060c \u0642\u0637\u0639\u0627\u064b \u0628\u0627\u06cc\u062f \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0622\u0646 \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u062f <code>numpy<\/code> \u0627\u0633\u0646\u0627\u062f\u06cc \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0622\u06cc\u0627 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631 <code>numpy<\/code> \u0631\u0648\u0634 \u0637\u0631\u0627\u062d\u06cc \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0634\u06a9\u0644 \u0634\u0645\u0627  \u0634\u0627\u0646\u0633 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f!<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0628\u0631\u0627\u06cc \u06a9\u0645\u06a9 \u0628\u0647 \u062a\u06a9\u0631\u0627\u0631 process \u0628\u0627 \u0646\u0642\u0627\u0637 \u0645\u0631\u06a9\u0632\u06cc \u062c\u062f\u06cc\u062f\u0645\u0627\u0646\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u06a9\u062f \u0642\u0628\u0644\u06cc \u062e\u0648\u062f \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0646\u06cc\u0645\u060c \u0622\u0646 \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0622\u06cc\u0627 \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a\u06cc \u062f\u0631 \u0631\u0648\u0634 \u06af\u0631\u0648\u0647 \u0628\u0646\u062f\u06cc \u0646\u0642\u0627\u0637 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">assigns_points_to_two_groups<\/span>(<span class=\"hljs-params\">g1_center, g2_center<\/span>):<\/span>\n    points_in_g1 = ()\n    points_in_g2 = ()\n    group = ()\n\n    <span class=\"hljs-keyword\">for<\/span> p <span class=\"hljs-keyword\">in<\/span> points:\n        x1, y1 = p(<span class=\"hljs-number\">0<\/span>), p(<span class=\"hljs-number\">1<\/span>)\n        euclidean_distance_g1 = np.sqrt((g1_center(<span class=\"hljs-number\">0<\/span>) - x1)**<span class=\"hljs-number\">2<\/span> + (g1_center(<span class=\"hljs-number\">1<\/span>) - y1)**<span class=\"hljs-number\">2<\/span>)\n        euclidean_distance_g2 = np.sqrt((g2_center(<span class=\"hljs-number\">0<\/span>) - x1)**<span class=\"hljs-number\">2<\/span> + (g2_center(<span class=\"hljs-number\">1<\/span>) - y1)**<span class=\"hljs-number\">2<\/span>)\n        <span class=\"hljs-keyword\">if<\/span> euclidean_distance_g1 &lt; euclidean_distance_g2:\n            points_in_g1.append(p)\n            group.append(<span class=\"hljs-number\">1<\/span>)\n        <span class=\"hljs-keyword\">else<\/span>:\n            points_in_g2.append(p)\n            group.append(<span class=\"hljs-number\">2<\/span>)\n    <span class=\"hljs-keyword\">return<\/span> points_in_g1, points_in_g2, group\n<\/code><\/pre>\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> \u0627\u06af\u0631 \u0645\u062a\u0648\u062c\u0647 \u0634\u062f\u06cc\u062f \u06a9\u0647 \u06cc\u06a9 \u06a9\u062f \u0631\u0627 \u0628\u0627\u0631\u0647\u0627 \u0648 \u0628\u0627\u0631\u0647\u0627 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u062f\u060c \u0628\u0627\u06cc\u062f \u0622\u0646 \u06a9\u062f \u0631\u0627 \u062f\u0631 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u0628\u067e\u06cc\u0686\u06cc\u062f.  \u0633\u0627\u0632\u0645\u0627\u0646\u062f\u0647\u06cc \u06a9\u062f \u0628\u0647 \u062a\u0648\u0627\u0628\u0639 \u0628\u0647\u062a\u0631\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0645\u06cc \u0634\u0648\u062f\u060c \u0628\u0647 \u0648\u06cc\u0698\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u06a9\u0647 \u062a\u0633\u062a \u0631\u0627 \u062a\u0633\u0647\u06cc\u0644 \u0645\u06cc \u06a9\u0646\u062f.  \u0622\u0632\u0645\u0627\u06cc\u0634 \u06cc\u06a9 \u0642\u0637\u0639\u0647 \u06a9\u062f \u062c\u062f\u0627 \u0634\u062f\u0647 \u0627\u0632 \u06cc\u06a9 \u06a9\u062f \u06a9\u0627\u0645\u0644 \u0628\u062f\u0648\u0646 \u0647\u06cc\u0686 \u0639\u0645\u0644\u06a9\u0631\u062f\u06cc \u0622\u0633\u0627\u0646 \u062a\u0631 \u0627\u0633\u062a.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u062a\u0627\u0628\u0639 \u0631\u0627 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0646\u062a\u0627\u06cc\u062c \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0622\u0646 \u0630\u062e\u06cc\u0631\u0647 \u06a9\u0646\u06cc\u0645 <code>points_in_g1<\/code>\u060c <code>points_in_g2<\/code>\u060c \u0648 <code>group<\/code> \u0645\u062a\u063a\u06cc\u0631\u0647\u0627:<\/p>\n<pre><code class=\"hljs\">points_in_g1, points_in_g2, group = assigns_points_to_two_groups(g1_center, g2_center)\npoints_in_g1, points_in_g2, group\n<\/code><\/pre>\n<p>\u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0646\u0645\u0648\u062f\u0627\u0631 \u067e\u0631\u0627\u06a9\u0646\u062f\u06af\u06cc \u0631\u0627 \u0628\u0627 \u0646\u0642\u0627\u0637 \u0631\u0646\u06af\u06cc \u062a\u0631\u0633\u06cc\u0645 \u06a9\u0646\u06cc\u062f \u062a\u0627 \u062a\u0642\u0633\u06cc\u0645 \u06af\u0631\u0648\u0647 \u0647\u0627 \u0631\u0627 \u062a\u062c\u0633\u0645 \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\">sns.scatterplot(x=points(:, <span class=\"hljs-number\">0<\/span>), y=points(:, <span class=\"hljs-number\">1<\/span>), hue=group)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-5.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0646\u0642\u0627\u0637 \u0645\u0627 \u0627\u0633\u062a <em>\u0628\u0647\u062a\u0631 \u0634\u062f\u0646<\/em>.  \u0627\u0645\u0627 \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u062f\u0648 \u0646\u0642\u0637\u0647 \u062f\u0631 \u0648\u0633\u0637 \u0646\u0645\u0648\u062f\u0627\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u06af\u0631\u0648\u0647\u200c\u0647\u0627 \u062f\u0631 \u0645\u062c\u0627\u0648\u0631\u062a \u0647\u0631 \u062f\u0648 \u06af\u0631\u0648\u0647 \u0646\u0633\u0628\u062a \u062f\u0627\u062f.  \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc \u06a9\u0647 \u0645\u0627 \u062a\u0627\u06a9\u0646\u0648\u0646 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645\u060c \u0647\u0631 \u062f\u0648\u06cc \u0627\u06cc\u0646 \u0646\u0642\u0627\u0637 \u0631\u0627 \u0628\u0647 \u06af\u0631\u0648\u0647 \u062f\u0648\u0645 \u0627\u062e\u062a\u0635\u0627\u0635 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<p>\u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u0627 \u0627\u062d\u062a\u0645\u0627\u0644\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0646 \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u06a9\u0646\u06cc\u0645 process \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u06cc\u06af\u0631 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc Xs \u0648 Ys\u060c \u0627\u06cc\u062c\u0627\u062f \u062f\u0648 \u0646\u0642\u0637\u0647 \u0645\u0631\u06a9\u0632\u06cc \u062c\u062f\u06cc\u062f <em><strong>(\u0633\u0646\u062a\u0631\u0648\u0626\u06cc\u062f\u0647\u0627)<\/strong><\/em>  \u0628\u0647 \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc \u0645\u0627 \u0648 \u062a\u062e\u0635\u06cc\u0635 \u0645\u062c\u062f\u062f \u0622\u0646\u0647\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0631\u0648\u06cc \u0641\u0627\u0635\u0644\u0647<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0628\u0631\u0627\u06cc \u0628\u0647 \u0631\u0648\u0632 \u0631\u0633\u0627\u0646\u06cc \u0633\u0627\u0646\u062a\u0631\u0648\u0626\u06cc\u062f\u0647\u0627 \u0646\u06cc\u0632 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645.  \u062a\u0645\u0627\u0645 process \u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0686\u0646\u062f\u06cc\u0646 \u062a\u0645\u0627\u0633 \u0622\u0646 \u062a\u0627\u0628\u0639 \u06a9\u0627\u0647\u0634 \u062f\u0627\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">updates_centroids<\/span>(<span class=\"hljs-params\">points_in_g1, points_in_g2<\/span>):<\/span>\n    g1_center = np.array(points_in_g1)(:, <span class=\"hljs-number\">0<\/span>).mean(), np.array(points_in_g1)(:, <span class=\"hljs-number\">1<\/span>).mean()\n    g2_center = np.array(points_in_g2)(:, <span class=\"hljs-number\">0<\/span>).mean(), np.array(points_in_g2)(:, <span class=\"hljs-number\">1<\/span>).mean()\n    <span class=\"hljs-keyword\">return<\/span> g1_center, g2_center\n\ng1_center, g2_center = updates_centroids(points_in_g1, points_in_g2)\npoints_in_g1, points_in_g2, group = assigns_points_to_two_groups(g1_center, g2_center)\nsns.scatterplot(x=points(:, <span class=\"hljs-number\">0<\/span>), y=points(:, <span class=\"hljs-number\">1<\/span>), hue=group)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-6.png\" alt=\"\" title=\"\"><\/p>\n<p>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u067e\u0633 \u0627\u0632 \u0627\u06cc\u0646 \u062a\u06a9\u0631\u0627\u0631 \u0633\u0648\u0645\u060c \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0646\u0642\u0627\u0637 \u0627\u06a9\u0646\u0648\u0646 \u0628\u0647 \u062e\u0648\u0634\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u062a\u0639\u0644\u0642 \u062f\u0627\u0631\u0646\u062f.  \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u06a9\u0647 \u0646\u062a\u0627\u06cc\u062c \u0628\u0647\u062a\u0631 \u0645\u06cc \u0634\u0648\u062f &#8211; \u0628\u06cc\u0627\u06cc\u06cc\u062f \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u06cc\u06af\u0631 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645.  \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0631\u0641\u062a\u0646 \u0628\u0647 <em>\u062a\u06a9\u0631\u0627\u0631 \u0686\u0647\u0627\u0631\u0645<\/em> \u0631\u0648\u0634 \u0645\u0627:<\/p>\n<pre><code class=\"hljs\">g1_center, g2_center = updates_centroids(points_in_g1, points_in_g2)\npoints_in_g1, points_in_g2, group = assigns_points_to_two_groups(g1_center, g2_center)\nsns.scatterplot(x=points(:, <span class=\"hljs-number\">0<\/span>), y=points(:, <span class=\"hljs-number\">1<\/span>), hue=group)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-7.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0627\u06cc\u0646 \u0686\u0647\u0627\u0631\u0645\u06cc\u0646 \u0628\u0627\u0631 \u0631\u0633\u06cc\u062f\u06cc\u0645 <em>\u0647\u0645\u0627\u0646 \u0646\u062a\u06cc\u062c\u0647<\/em> \u0645\u0627\u0646\u0646\u062f \u0642\u0628\u0644\u06cc  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u0627\u0645\u062a\u06cc\u0627\u0632\u0627\u062a \u0645\u0627 \u062f\u06cc\u06af\u0631 \u06af\u0631\u0648\u0647 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc \u062f\u0647\u062f\u060c \u0646\u062a\u06cc\u062c\u0647 \u0645\u0627 \u0628\u0647 \u0646\u0648\u0639\u06cc \u062b\u0628\u0627\u062a \u0631\u0633\u06cc\u062f\u0647 \u0627\u0633\u062a &#8211; \u0628\u0647 \u062d\u0627\u0644\u062a \u063a\u06cc\u0631\u0642\u0627\u0628\u0644 \u062a\u063a\u06cc\u06cc\u0631 \u0631\u0633\u06cc\u062f\u0647 \u0627\u0633\u062a\u060c \u06cc\u0627 <strong>\u0647\u0645\u06af\u0631\u0627 \u0634\u062f<\/strong>.  \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646\u060c \u062f\u0642\u06cc\u0642\u0627\u064b \u0647\u0645\u0627\u0646 \u0646\u062a\u06cc\u062c\u0647 \u0627\u06cc \u0631\u0627 \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u06cc 2 \u06af\u0631\u0648\u0647 \u0645\u062a\u0635\u0648\u0631 \u0628\u0648\u062f\u06cc\u0645.  \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u0627\u06cc\u0646 \u062a\u0642\u0633\u06cc\u0645 \u0628\u0646\u062f\u06cc \u0645\u0646\u0637\u0642\u06cc \u0627\u0633\u062a \u06cc\u0627 \u062e\u06cc\u0631.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u0633\u0631\u0639\u062a \u06a9\u0627\u0631\u0647\u0627\u06cc\u06cc \u0631\u0627 \u06a9\u0647 \u062a\u0627\u06a9\u0646\u0648\u0646 \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f\u0647\u200c\u0627\u06cc\u0645 \u0645\u0631\u0648\u0631 \u06a9\u0646\u06cc\u0645.  \u0645\u0627 10 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u062e\u0648\u062f \u0631\u0627 \u0627\u0632 \u0646\u0638\u0631 \u062c\u063a\u0631\u0627\u0641\u06cc\u0627\u06cc\u06cc \u0628\u0647 \u062f\u0648 \u0628\u062e\u0634 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 &#8211; \u06cc\u06a9\u06cc \u062f\u0631 \u0645\u0646\u0627\u0637\u0642 \u062c\u0646\u0648\u0628 \u063a\u0631\u0628\u06cc \u067e\u0627\u06cc\u06cc\u0646 \u0648 \u0628\u0642\u06cc\u0647 \u062f\u0631 \u0634\u0645\u0627\u0644 \u0634\u0631\u0642\u06cc.  \u062c\u0645\u0639\u200c\u0622\u0648\u0631\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0628\u06cc\u0634\u062a\u0631 \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0622\u0646\u0686\u0647 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u062f\u0627\u0631\u06cc\u0645 &#8211; \u062f\u0631\u0622\u0645\u062f\u060c \u062a\u0639\u062f\u0627\u062f \u0631\u0648\u0632\u0627\u0646\u0647 \u0645\u0634\u062a\u0631\u06cc\u0627\u0646 \u0648 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0645\u0648\u0627\u0631\u062f \u062f\u06cc\u06af\u0631\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u062c\u0627\u0644\u0628 \u0628\u0627\u0634\u062f.  \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u063a\u0646\u06cc\u200c\u062a\u0631\u06cc \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 \u0648 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u0646\u062a\u0627\u06cc\u062c \u062c\u0627\u0644\u0628\u200c\u062a\u0631\u06cc \u062a\u0648\u0644\u06cc\u062f \u06a9\u0646\u06cc\u0645.<\/p>\n<blockquote>\n<p>\u0645\u0637\u0627\u0644\u0639\u0627\u062a \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0645\u0627\u0646\u0646\u062f \u0627\u06cc\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0632\u0645\u0627\u0646\u06cc \u0627\u0646\u062c\u0627\u0645 \u0634\u0648\u062f \u06a9\u0647 \u06cc\u06a9 \u0628\u0631\u0646\u062f \u0627\u0632 \u0642\u0628\u0644 \u062a\u0627\u0633\u06cc\u0633 \u0634\u062f\u0647 \u0628\u062e\u0648\u0627\u0647\u062f \u0645\u0646\u0637\u0642\u0647\u200c\u0627\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u0641\u062a\u062a\u0627\u062d \u06cc\u06a9 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u062c\u062f\u06cc\u062f \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u062f.  \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f\u060c \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0628\u06cc\u0634\u062a\u0631\u06cc \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0645\u06a9\u0627\u0646 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<\/blockquote>\n<h3 id=\"whatdoesallthishavetodowithkmeansalgorithm\"><span class=\"ez-toc-section\" id=\"%d9%87%d9%85%d9%87_%d8%a7%db%8c%d9%86%d9%87%d8%a7_%da%86%d9%87_%d8%b1%d8%a8%d8%b7%db%8c_%d8%a8%d9%87_%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85_k-means_%d8%af%d8%a7%d8%b1%d8%af%d8%9f\"><\/span>\u0647\u0645\u0647 \u0627\u06cc\u0646\u0647\u0627 \u0686\u0647 \u0631\u0628\u0637\u06cc \u0628\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u062f\u0627\u0631\u062f\u061f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0627\u06cc\u0646 \u0645\u0631\u0627\u062d\u0644 \u0631\u0627 \u062f\u0646\u0628\u0627\u0644 \u0645\u06cc \u06a9\u0646\u06cc\u062f\u060c \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u062a\u0639\u062c\u0628 \u06a9\u0631\u062f\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0622\u0646\u0647\u0627 \u0686\u0647 \u0627\u0631\u062a\u0628\u0627\u0637\u06cc \u0628\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u062f\u0627\u0631\u0646\u062f.  \u0631\u0627 process \u0645\u0627 \u062a\u0627\u06a9\u0646\u0648\u0646 \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f\u0647 \u0627\u06cc\u0645 <strong>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means<\/strong>.  \u0628\u0647 \u0637\u0648\u0631 \u062e\u0644\u0627\u0635\u0647\u060c \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0648\u0647\u200c\u0647\u0627\/\u062e\u0648\u0634\u0647\u200c\u0647\u0627\u060c \u0646\u0642\u0627\u0637 \u0627\u0648\u0644\u06cc\u0647 \u0631\u0627 \u0628\u0647\u200c\u0637\u0648\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u0647\u200c\u0627\u06cc\u0645\u060c \u0648 \u0645\u0631\u06a9\u0632\u0647\u0627 \u0631\u0627 \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u062e\u0648\u0634\u0647\u200c\u0647\u0627 \u0647\u0645\u06af\u0631\u0627 \u0634\u0648\u0646\u062f\u060c \u0628\u0647\u200c\u0631\u0648\u0632\u0631\u0633\u0627\u0646\u06cc \u06a9\u0631\u062f\u0647\u200c\u0627\u06cc\u0645.  \u0645\u0627 \u0627\u0633\u0627\u0633\u0627\u064b \u06a9\u0644 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0628\u0627 \u062f\u0633\u062a \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f\u0647 \u0627\u06cc\u0645 &#8211; \u0647\u0631 \u0645\u0631\u062d\u0644\u0647 \u0631\u0627 \u0628\u0627 \u062f\u0642\u062a \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645.<\/p>\n<p>\u0631\u0627 <em>\u06a9<\/em> \u062f\u0631 K-Means \u0627\u0632 <em>\u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627<\/em> \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0642\u0628\u0644 \u0627\u0632 \u0634\u0631\u0648\u0639 \u062a\u06a9\u0631\u0627\u0631 \u062a\u0646\u0638\u06cc\u0645 \u0634\u0648\u0646\u062f process.  \u062f\u0631 \u0645\u0648\u0631\u062f \u0645\u0627 <em>K = 2<\/em>.  \u0627\u06cc\u0646 \u0648\u06cc\u0698\u06af\u06cc \u06af\u0627\u0647\u06cc \u0627\u0648\u0642\u0627\u062a \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062f\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f <strong><em>\u0645\u0646\u0641\u06cc<\/em><\/strong>  \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u062f\u06cc\u06af\u0631\u06cc \u0645\u0627\u0646\u0646\u062f \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628\u06cc\u060c \u06a9\u0647 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u062f\u0627\u0634\u062a\u0646 \u062a\u0639\u062f\u0627\u062f \u062b\u0627\u0628\u062a\u06cc \u0627\u0632 \u062e\u0648\u0634\u0647\u200c\u0647\u0627 \u0627\u0632 \u0642\u0628\u0644 \u0646\u06cc\u0633\u062a.<\/p>\n<p>\u0628\u0647 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0648\u0633\u06cc\u0644\u0647\u060c K-means \u0646\u06cc\u0632 \u0645\u06cc \u0634\u0648\u062f <em>\u0646\u0633\u0628\u062a \u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u067e\u0631\u062a \u0648 \u0634\u062f\u06cc\u062f \u062d\u0633\u0627\u0633 \u0627\u0633\u062a<\/em> &#8211; \u0622\u0646\u0647\u0627 \u062a\u063a\u06cc\u06cc\u0631\u067e\u0630\u06cc\u0631\u06cc \u0631\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u0646\u062f \u0648 \u0627\u0646\u062c\u0627\u0645 \u0646\u0642\u0634 \u062e\u0648\u062f \u0631\u0627 \u0628\u0631\u0627\u06cc \u0645\u0631\u06a9\u0632\u0647\u0627\u06cc \u0645\u0627 \u062f\u0634\u0648\u0627\u0631\u062a\u0631 \u0645\u06cc \u06a9\u0646\u0646\u062f.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0627\u0632 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0627\u062c\u0631\u0627 \u0622\u06af\u0627\u0647 \u0628\u0627\u0634\u06cc\u062f <em>\u0645\u0642\u0627\u062f\u06cc\u0631 \u0634\u062f\u06cc\u062f \u0648 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0628\u06cc\u0631\u0648\u0646\u06cc<\/em> \u0642\u0628\u0644 \u0627\u0632 \u0627\u0646\u062c\u0627\u0645 \u06cc\u06a9 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means.<\/p>\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0646\u0642\u0627\u0637 \u0645\u0627 \u062f\u0631 \u0642\u0633\u0645\u062a \u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u06cc\u0645 \u062a\u0642\u0633\u06cc\u0645 \u0634\u062f\u0647 \u0627\u0646\u062f\u060c \u0647\u0646\u06af\u0627\u0645 \u0627\u06cc\u062c\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627 \u0645\u0646\u062d\u0646\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f.  \u0627\u06cc\u0646 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0636\u0639\u0641 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u0628\u0627\u0634\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> \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0628\u0647 \u0627\u0646\u0639\u0637\u0627\u0641 \u067e\u0630\u06cc\u0631\u06cc \u0648 \u0633\u0627\u0632\u06af\u0627\u0631\u06cc \u0628\u06cc\u0634\u062a\u0631 \u0628\u0627 \u0628\u06cc\u0636\u06cc \u0647\u0627 \u0648 \u0627\u0634\u06a9\u0627\u0644 \u062f\u06cc\u06af\u0631 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u062f\u060c \u0633\u0639\u06cc \u06a9\u0646\u06cc\u062f \u0627\u0632 a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f <em>\u062a\u0639\u0645\u06cc\u0645 K-means \u0645\u062f\u0644 \u0645\u062e\u0644\u0648\u0637 \u06af\u0627\u0648\u0633\u06cc<\/em>.  \u0627\u06cc\u0646 \u0645\u062f\u0644 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0627 \u062e\u0648\u0634\u0647 \u0647\u0627\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0628\u0646\u062f\u06cc \u0628\u06cc\u0636\u0648\u06cc \u0633\u0627\u0632\u06af\u0627\u0631 \u0634\u0648\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>K-Means \u0646\u06cc\u0632 \u0628\u0633\u06cc\u0627\u0631\u06cc \u062f\u0627\u0631\u062f <strong><em>\u0645\u0632\u0627\u06cc\u0627\u06cc<\/em><\/strong>!  \u0639\u0645\u0644\u06a9\u0631\u062f \u062e\u0648\u0628\u06cc \u062f\u0627\u0631\u062f \u0631\u0648\u06cc <em>\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af<\/em> \u0627\u06af\u0631 \u0627\u0632 \u0627\u0646\u0648\u0627\u0639 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u062f\u060c \u0631\u0633\u06cc\u062f\u06af\u06cc \u0628\u0647 \u0622\u0646 \u062f\u0634\u0648\u0627\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f.  \u0622\u0646 \u0631\u0627 \u0646\u06cc\u0632 <em>\u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u0631\u0627 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f<\/em>\u060c \u0648 \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f <em>\u062a\u0639\u0645\u06cc\u0645 \u062f\u0627\u062f\u0646<\/em> \u0648 <em>\u0633\u0627\u0632\u06af\u0627\u0631 \u0634\u062f\u0646<\/em>.  \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0622\u0646\u060c \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u067e\u0631\u06a9\u0627\u0631\u0628\u0631\u062f\u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0627\u0633\u062a.<\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u06a9\u0647 \u062a\u0645\u0627\u0645 \u0645\u0631\u0627\u062d\u0644 \u0627\u0646\u062c\u0627\u0645 \u0634\u062f\u0647 \u062f\u0631 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u0631\u0627 \u0645\u0631\u0648\u0631 \u06a9\u0631\u062f\u06cc\u0645 \u0648 \u062a\u0645\u0627\u0645 \u062c\u0648\u0627\u0646\u0628 \u0645\u062b\u0628\u062a \u0648 \u0645\u0646\u0641\u06cc \u0622\u0646 \u0631\u0627 \u0641\u0647\u0645\u06cc\u062f\u06cc\u0645\u060c \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 K-Means \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Scikit-Learn \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<h2 id=\"howtoimplementkmeansalgorithmusingscikitlearn\"><span class=\"ez-toc-section\" id=\"%d8%b1%d9%88%d8%b4_%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_%d8%a7%d9%84%da%af%d9%88%d8%b1%db%8c%d8%aa%d9%85_k-means_%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>\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <em>Scikit-Learn<\/em><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u0645\u062c\u062f\u062f \u0646\u062a\u06cc\u062c\u0647\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 process \u062f\u0648\u0628\u0627\u0631\u0647\u060c \u0627\u0645\u0627 \u0627\u06a9\u0646\u0648\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 3 \u062e\u0637 \u06a9\u062f \u0628\u0627 <code>sklearn<\/code>:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">from<\/span> sklearn.cluster <span class=\"hljs-keyword\">import<\/span> KMeans\n\n\nkmeans = KMeans(n_clusters=<span class=\"hljs-number\">2<\/span>, random_state=<span class=\"hljs-number\">42<\/span>) \nkmeans.fit(points)\nkmeans.labels_\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627\u060c \u0628\u0631\u0686\u0633\u0628 \u0647\u0627 \u0645\u0627\u0646\u0646\u062f \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc \u0642\u0628\u0644\u06cc \u0645\u0627 \u0647\u0633\u062a\u0646\u062f.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u0633\u0631\u0639\u062a \u0646\u062a\u06cc\u062c\u0647 \u0631\u0627 \u062a\u0631\u0633\u06cc\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">sns.scatterplot(x = points(:,<span class=\"hljs-number\">0<\/span>), y = points(:,<span class=\"hljs-number\">1<\/span>), hue=kmeans.labels_)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-8.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0647\u0645\u0627\u0646\u0646\u062f \u062a\u0635\u0648\u06cc\u0631 \u0628\u062e\u0634 \u0642\u0628\u0644 \u0627\u0633\u062a.<\/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> \u0641\u0642\u0637 \u0646\u06af\u0627\u0647 \u06a9\u0631\u062f\u0646 \u0628\u0647 \u0631\u0648\u0634 \u0627\u062c\u0631\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u0647 \u0634\u0645\u0627 \u0627\u06cc\u0646 \u062a\u0635\u0648\u0631 \u0631\u0627 \u0628\u062f\u0647\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0628\u06cc\u0647\u0648\u062f\u0647 \u0627\u0633\u062a \u0648 \u0646\u06cc\u0627\u0632\u06cc \u0646\u06cc\u0633\u062a \u06a9\u0647 \u0632\u06cc\u0627\u062f \u0646\u06af\u0631\u0627\u0646 \u0622\u0646 \u0628\u0627\u0634\u06cc\u062f.  \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u06af\u0627\u0645 \u0628\u0647 \u06af\u0627\u0645 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f\u06cc\u0645\u060c \u0641\u0642\u0637 3 \u062e\u0637 \u06a9\u062f \u062a\u0645\u0627\u0645 \u0645\u0631\u0627\u062d\u0644\u06cc \u0631\u0627 \u06a9\u0647 \u062f\u0631 \u0628\u062e\u0634 \u0642\u0628\u0644 \u062f\u0631 \u0645\u0648\u0631\u062f \u0622\u0646 \u0635\u062d\u0628\u062a \u06a9\u0631\u062f\u06cc\u0645 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u062f.  \u0648\u0644\u06cc\u060c <em><strong>\u0634\u06cc\u0637\u0627\u0646 \u062f\u0631 \u062c\u0632\u0626\u06cc\u0627\u062a \u0627\u0633\u062a<\/strong><\/em>  \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f!  \u0627\u06af\u0631 \u062a\u0645\u0627\u0645 \u0645\u0631\u0627\u062d\u0644 \u0648 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a \u0647\u0627\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u062f\u0631\u06a9 \u0646\u06a9\u0646\u06cc\u062f\u060c \u0628\u0647 \u0627\u062d\u062a\u0645\u0627\u0644 \u0632\u06cc\u0627\u062f \u0628\u0627 \u0645\u0648\u0642\u0639\u06cc\u062a\u06cc \u0645\u0648\u0627\u062c\u0647 \u062e\u0648\u0627\u0647\u06cc\u062f \u0634\u062f \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u0646\u062a\u0627\u06cc\u062c\u06cc \u0631\u0627 \u0628\u0647 \u0634\u0645\u0627 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0627\u0646\u062a\u0638\u0627\u0631\u0634 \u0631\u0627 \u0646\u062f\u0627\u0634\u062a\u06cc\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0628\u0627 Scikit-Learn\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f K-Means \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u0633\u0631\u06cc\u0639\u200c\u062a\u0631 \u0628\u0627 \u062a\u0646\u0638\u06cc\u0645 <code>init='k-means++'<\/code> \u0628\u062d\u062b \u0648 \u062c\u062f\u0644.  \u0628\u0647 \u0639\u0628\u0627\u0631\u062a\u06cc \u06af\u0633\u062a\u0631\u062f\u0647 \u062a\u0631\u060c <em>K-Means++<\/em> \u0647\u0646\u0648\u0632 \u0647\u0645 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u06a9\u0646\u062f <em>\u06a9<\/em> \u0645\u0631\u06a9\u0632 \u062e\u0648\u0634\u0647 \u0627\u0648\u0644\u06cc\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u062a\u0635\u0627\u062f\u0641\u06cc \u067e\u0633 \u0627\u0632 \u062a\u0648\u0632\u06cc\u0639 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a.  \u0633\u067e\u0633\u060c \u0647\u0631 \u0645\u0631\u06a9\u0632 \u062e\u0648\u0634\u0647 \u0628\u0639\u062f\u06cc \u0627\u0632 \u0645\u06cc\u0627\u0646 \u0646\u0642\u0627\u0637 \u062f\u0627\u062f\u0647 \u0628\u0627\u0642\u06cc\u0645\u0627\u0646\u062f\u0647 \u0646\u0647 \u0628\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0641\u0627\u0635\u0644\u0647 &#8211; \u0628\u0644\u06a9\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u062d\u062a\u0645\u0627\u0644\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0633\u0631\u0639\u062a \u0645\u06cc \u0628\u062e\u0634\u062f \u0648 \u062f\u0631 \u0647\u0646\u06af\u0627\u0645 \u0628\u0631\u062e\u0648\u0631\u062f \u0628\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0628\u0632\u0631\u06af \u0645\u0641\u06cc\u062f \u0627\u0633\u062a.<\/p>\n<h2 id=\"theelbowmethodchoosingthebestnumberofgroups\"><span class=\"ez-toc-section\" id=\"%d8%b1%d9%88%d8%b4_%d8%a2%d8%b1%d9%86%d8%ac_%e2%80%93_%d8%a7%d9%86%d8%aa%d8%ae%d8%a7%d8%a8_%d8%a8%d9%87%d8%aa%d8%b1%db%8c%d9%86_%d8%aa%d8%b9%d8%af%d8%a7%d8%af_%da%af%d8%b1%d9%88%d9%87\"><\/span>\u0631\u0648\u0634 \u0622\u0631\u0646\u062c &#8211; \u0627\u0646\u062a\u062e\u0627\u0628 \u0628\u0647\u062a\u0631\u06cc\u0646 \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0648\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062a\u0627 \u0627\u06cc\u0646\u062c\u0627\u06cc \u06a9\u0627\u0631 \u062e\u06cc\u0644\u06cc \u062e\u0648\u0628\u0647!  \u0645\u0627 10 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 \u0631\u0648\u06cc \u0641\u0627\u0635\u0644\u0647 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0628\u06cc\u0646 \u0646\u0642\u0627\u0637 \u0648 \u0645\u0631\u06a9\u0632.  \u0627\u0645\u0627 \u062f\u0631 \u0645\u0648\u0631\u062f \u0622\u0646 \u062f\u0648 \u0646\u0642\u0637\u0647 \u062f\u0631 \u0648\u0633\u0637 \u0646\u0645\u0648\u062f\u0627\u0631 \u06a9\u0647 \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0622\u0646\u200c\u0647\u0627 \u06a9\u0645\u06cc \u0633\u062e\u062a\u200c\u062a\u0631 \u0627\u0633\u062a\u060c \u0686\u0637\u0648\u0631\u061f  \u0622\u06cc\u0627 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646\u0633\u062a\u0646\u062f \u06cc\u06a9 \u06af\u0631\u0648\u0647 \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u0647\u0645 \u062a\u0634\u06a9\u06cc\u0644 \u062f\u0647\u0646\u062f\u061f  \u0622\u06cc\u0627 \u0648\u0627\u0642\u0639\u0627\u064b \u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u0634\u062a\u0628\u0627\u0647 \u06a9\u0631\u062f\u06cc\u0645\u061f <em>K=2<\/em> \u06af\u0631\u0648\u0647 \u0647\u0627\u061f  \u0634\u0627\u06cc\u062f \u0648\u0627\u0642\u0639\u0627 \u062f\u0627\u0634\u062a\u06cc\u0645 <em>K=3<\/em> \u06af\u0631\u0648\u0647 \u0647\u0627\u061f  \u062d\u062a\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u0633\u062a\u06cc\u0645 \u0628\u06cc\u0634 \u0627\u0632 \u0633\u0647 \u06af\u0631\u0648\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645 \u0648 \u0627\u0632 \u0622\u0646 \u0622\u06af\u0627\u0647 \u0646\u0628\u0627\u0634\u06cc\u0645.<\/p>\n<p>\u0633\u0648\u0627\u0644\u06cc \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0645\u0637\u0631\u062d \u0645\u06cc \u0634\u0648\u062f \u0627\u06cc\u0646 \u0627\u0633\u062a <em><strong>\u0631\u0648\u0634 \u062a\u0639\u06cc\u06cc\u0646 \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0648\u0647 \u0647\u0627 (K) \u062f\u0631 K-Means<\/strong><\/em>.  \u0628\u0631\u0627\u06cc \u067e\u0627\u0633\u062e \u0628\u0647 \u0627\u06cc\u0646 \u0633\u0648\u0627\u0644\u060c \u0628\u0627\u06cc\u062f \u0628\u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u062e\u0648\u0634\u0647 &#8220;\u0628\u0647\u062a\u0631&#8221; \u0628\u0631\u0627\u06cc \u0645\u0642\u062f\u0627\u0631 \u0645\u062a\u0641\u0627\u0648\u062a K \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631.<\/p>\n<p>\u0631\u0627\u0647 \u0633\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0622\u0646\u060c \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0646\u0642\u0627\u0637 \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062e\u062a\u0644\u0641 \u0627\u0633\u062a <em>\u06a9<\/em>\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0628\u0631\u0627\u06cc <em>K=2\u060c K=3\u060c K=4\u060c \u0648 \u063a\u06cc\u0631\u0647 \u0631\u0648\u06cc<\/em>:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">for<\/span> number_of_clusters <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">11<\/span>): \n    kmeans = KMeans(n_clusters = number_of_clusters, random_state = <span class=\"hljs-number\">42<\/span>)\n    kmeans.fit(points) \n<\/code><\/pre>\n<p>\u0627\u0645\u0627\u060c \u0646\u0642\u0627\u0637 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0628\u0631\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 <em>Ks<\/em> \u062a\u0646\u0647\u0627 <em>\u06a9\u0627\u0641\u06cc \u0646\u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f<\/em> \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0627\u06cc\u0646\u06a9\u0647 \u0622\u06cc\u0627 \u0645\u0642\u062f\u0627\u0631 \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0622\u0646 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 \u06cc\u0627 \u062e\u06cc\u0631 <em>\u06a9<\/em>.  \u0645\u0627 \u0628\u0647 \u0631\u0627\u0647\u06cc \u0628\u0631\u0627\u06cc \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u06a9\u06cc\u0641\u06cc\u062a \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u06a9 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645 <em>\u06a9<\/em> \u0645\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645<\/p>\n<h3 id=\"manuallycalculatingthewithinclustersumofsquareswcss\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87_%d8%af%d8%b3%d8%aa%db%8c_%d8%af%d8%b1%d9%88%d9%86_%d9%85%d8%ac%d9%85%d9%88%d8%b9_%d9%85%d8%b1%d8%a8%d8%b9%e2%80%8c%d9%87%d8%a7_wcss\"><\/span>\u0645\u062d\u0627\u0633\u0628\u0647 \u062f\u0633\u062a\u06cc <em>\u062f\u0631\u0648\u0646 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u200c\u0647\u0627 (WCSS)<\/em><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0645\u06a9\u0627\u0646 \u0627\u06cc\u062f\u0647 \u0622\u0644\u06cc \u0628\u0631\u0627\u06cc \u0645\u0639\u0631\u0641\u06cc \u0645\u06cc\u0632\u0627\u0646 \u0646\u0632\u062f\u06cc\u06a9\u06cc \u0646\u0642\u0627\u0637 \u062e\u0648\u0634\u0647 \u0627\u06cc \u0645\u0627 \u0628\u0647 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0627\u0633\u062a.  \u0627\u0633\u0627\u0633\u0627\u064b \u062a\u0648\u0636\u06cc\u062d \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0686\u0642\u062f\u0631 <em>\u0648\u0627\u0631\u06cc\u0627\u0646\u0633<\/em> \u0645\u0627 \u062f\u0631\u0648\u0646 \u06cc\u06a9 \u062e\u0648\u0634\u0647 \u0648\u0627\u062d\u062f \u062f\u0627\u0631\u06cc\u0645.  \u0627\u06cc\u0646 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f <strong>\u062f\u0631 \u0645\u062c\u0645\u0648\u0639 \u0645\u062c\u0630\u0648\u0631\u0627\u062a \u062e\u0648\u0634\u0647 \u0627\u06cc<\/strong>\u060c \u06cc\u0627 <em><strong>WCSS<\/strong><\/em>  \u0628\u0647 \u0637\u0648\u0631 \u062e\u0644\u0627\u0635\u0647  \u0647\u0631\u0686\u0647 WCSS \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0628\u0627\u0634\u062f\u060c \u0646\u0642\u0627\u0637 \u0645\u0627 \u0628\u0647 \u0647\u0645 \u0646\u0632\u062f\u06cc\u06a9\u062a\u0631 \u0647\u0633\u062a\u0646\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u0627 \u06cc\u06a9 \u062e\u0648\u0634\u0647 \u062e\u0648\u0634 \u0641\u0631\u0645 \u062a\u0631 \u062f\u0627\u0631\u06cc\u0645.  \u0641\u0631\u0645\u0648\u0644 WCSS \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u06cc \u0647\u0631 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f:<\/p>\n<p>$$<br \/>WCSS = \\sum(Pi_1 &#8211; Centroid_1)^2 + \\cdots + \\sum(Pi_n &#8211; Centroid_n)^2<br \/>$$<\/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\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627\u060c \u0645\u0627 \u0627\u0632 <em>\u0641\u0627\u0635\u0644\u0647 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc<\/em> \u0628\u0631\u0627\u06cc \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f\u0646 \u0645\u0631\u06a9\u0632\u060c \u0627\u0645\u0627 \u0633\u0627\u06cc\u0631 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u0641\u0627\u0635\u0644\u0647 \u0645\u0627\u0646\u0646\u062f \u0645\u0646\u0647\u062a\u0646 \u0646\u06cc\u0632 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u0646\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0641\u0631\u0636 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0648 \u06a9\u0644\u0627\u0633\u062a\u0631 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645 \u0648 \u0633\u0639\u06cc \u06a9\u0646\u06cc\u0645 WCSS \u0631\u0627 \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0647\u062a\u0631 \u0628\u0641\u0647\u0645\u06cc\u0645 WCSS \u0686\u06cc\u0633\u062a \u0648 \u0686\u06af\u0648\u0646\u0647 \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645.  \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0641\u0631\u0645\u0648\u0644 \u0628\u06cc\u0627\u0646 \u0645\u06cc \u06a9\u0646\u062f\u060c \u0645\u0627 \u0628\u0627\u06cc\u062f \u0645\u062c\u0630\u0648\u0631 \u0627\u062e\u062a\u0644\u0627\u0641 \u0628\u06cc\u0646 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u062e\u0648\u0634\u0647 \u0648 \u0645\u0631\u06a9\u0632 \u0631\u0627 \u062c\u0645\u0639 \u06a9\u0646\u06cc\u0645.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0627\u06af\u0631 \u0627\u0648\u0644\u06cc\u0646 \u0627\u0645\u062a\u06cc\u0627\u0632 \u0645\u0627 \u0627\u0632 \u06af\u0631\u0648\u0647 \u0627\u0648\u0644 \u0628\u0627\u0634\u062f <code>(5, 3)<\/code> \u0648 \u0622\u062e\u0631\u06cc\u0646 \u0645\u0631\u06a9\u0632 \u0645\u0627 (\u067e\u0633 \u0627\u0632 \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc) \u0627\u0632 \u06af\u0631\u0648\u0647 \u0627\u0648\u0644 \u0627\u0633\u062a <code>(16.8, 17.0)<\/code>\u060c WCSS \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f:<\/p>\n<p>$$<br \/>WCSS = \\sum((5\u060c3) &#8211; (16.8\u060c 17.0))^2<br \/>$$<\/p>\n<p>$$<br \/>WCSS = \\sum((5-16.8) + (3-17.0))^2<br \/>$$<\/p>\n<p>$$<br \/>WCSS = \\sum((-11.8) + (-14.0))^2<br \/>$$<\/p>\n<p>$$<br \/>WCSS = \\sum((-25.8))^2<br \/>$$<\/p>\n<p>$$<br \/>WCSS = 335.24<br \/>$$<\/p>\n<p>\u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 WCSS \u0631\u0627 \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0627\u0632 \u062e\u0648\u0634\u0647 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0627\u0645\u0627 \u062e\u0648\u0634\u0647 \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u0634\u0627\u0645\u0644 \u0628\u06cc\u0634 \u0627\u0632 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0627\u0633\u062a \u0648 \u0645\u0627 \u0628\u0627\u06cc\u062f \u0647\u0645\u0647 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0647\u0646\u06af\u0627\u0645 \u0645\u062d\u0627\u0633\u0628\u0647 WCSS \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645.  \u0645\u0627 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u062a\u0627\u0628\u0639\u06cc \u0627\u0646\u062c\u0627\u0645 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f \u06a9\u0647 \u062e\u0648\u0634\u0647 \u0627\u06cc \u0627\u0632 \u0646\u0642\u0627\u0637 \u0648 \u0645\u0631\u06a9\u0632\u0647\u0627 \u0631\u0627 \u062f\u0631\u06cc\u0627\u0641\u062a \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639 \u0647\u0627 \u0631\u0627 \u0628\u0631\u0645\u06cc \u06af\u0631\u062f\u0627\u0646\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">sum_of_squares<\/span>(<span class=\"hljs-params\">cluster, centroid<\/span>):<\/span>\n    squares = ()\n    <span class=\"hljs-keyword\">for<\/span> p <span class=\"hljs-keyword\">in<\/span> cluster:\n        squares.append((p - centroid)**<span class=\"hljs-number\">2<\/span>)\n        ss = np.array(squares).<span class=\"hljs-built_in\">sum<\/span>()\n    <span class=\"hljs-keyword\">return<\/span> ss\n<\/code><\/pre>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639 \u0647\u0627\u06cc \u0647\u0631 \u062e\u0648\u0634\u0647 \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">g1 = sum_of_squares(points_in_g1, g1_center)\ng2 = sum_of_squares(points_in_g2, g2_center)\n<\/code><\/pre>\n<p>\u0648 \u0646\u062a\u0627\u06cc\u062c \u0631\u0627 \u062c\u0645\u0639 \u06a9\u0646\u06cc\u062f \u062a\u0627 \u0645\u062c\u0645\u0648\u0639 \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u062f <em>WCSS<\/em>:<\/p>\n<pre><code class=\"hljs\">g1 + g2\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u062f\u0631:<\/p>\n<pre><code class=\"hljs\">2964.3999999999996\n<\/code><\/pre>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u062f\u0631 \u0645\u0648\u0631\u062f \u0645\u0627\u060c \u0686\u0647 \u0632\u0645\u0627\u0646\u06cc <em>\u06a9<\/em> \u0628\u0631\u0627\u0628\u0631 2\u060c \u0645\u062c\u0645\u0648\u0639 WCSS \u0627\u0633\u062a <em>2964.39<\/em>.  \u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 Ks \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u06cc\u0645 \u0648 WCSS \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u0622\u0646\u0647\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645.  \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628\u060c \u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u06cc\u0646\u0634\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f \u0686\u0647 \u0686\u06cc\u0632\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645 <em>\u06a9<\/em> \u0645\u0627 \u0628\u0627\u06cc\u062f \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0645\u0627 \u0628\u0647\u062a\u0631\u06cc\u0646 \u0639\u0645\u0644\u06a9\u0631\u062f \u0631\u0627 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/p>\n<h3 id=\"calculatingwcssusingscikitlearn\">\u062f\u0631 \u062d\u0627\u0644 \u0645\u062d\u0627\u0633\u0628\u0647 <em>WCSS<\/em> \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f\u0646 <em>Scikit-Learn<\/em><\/h3>\n<p>\u062e\u0648\u0634\u0628\u062e\u062a\u0627\u0646\u0647\u060c \u0645\u0627 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u0645\u062d\u0627\u0633\u0628\u0647 \u062f\u0633\u062a\u06cc WCSS \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u06a9 \u0646\u062f\u0627\u0631\u06cc\u0645 <em>\u06a9<\/em>.  \u067e\u0633 \u0627\u0632 \u0627\u0646\u062c\u0627\u0645 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc K-Means \u0628\u0631\u0627\u06cc \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0634\u062f\u0647\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 WCSS \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <code>inertia_<\/code> \u0635\u0641\u062a.  \u0627\u06a9\u0646\u0648\u0646\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0647 K-Means \u062e\u0648\u062f \u0628\u0631\u06af\u0631\u062f\u06cc\u0645 <code>for<\/code> \u062d\u0644\u0642\u0647\u060c \u0627\u0632 \u0622\u0646 \u0628\u0631\u0627\u06cc \u062a\u063a\u06cc\u06cc\u0631 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631 WCSS \u0645\u0631\u0628\u0648\u0637\u0647 \u0631\u0627 \u0641\u0647\u0631\u0633\u062a \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\">wcss = () \n<span class=\"hljs-keyword\">for<\/span> number_of_clusters <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">11<\/span>): \n    kmeans = KMeans(n_clusters = number_of_clusters, random_state = <span class=\"hljs-number\">42<\/span>)\n    kmeans.fit(points) \n    wcss.append(kmeans.inertia_)\nwcss\n<\/code><\/pre>\n<p>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0645\u0642\u062f\u0627\u0631 \u062f\u0648\u0645 \u062f\u0631 \u0644\u06cc\u0633\u062a \u062f\u0642\u06cc\u0642\u0627\u064b \u0647\u0645\u0627\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0642\u0628\u0644\u0627\u064b \u0628\u0631\u0627\u06cc \u0622\u0646 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0631\u062f\u0647 \u0628\u0648\u062f\u06cc\u0645 <em>K=2<\/em>:<\/p>\n<pre><code class=\"hljs\">(18272.9, # For k=1 \n 2964.3999999999996, # For k=2\n 1198.75, # For k=3\n 861.75,\n 570.5,\n 337.5,\n 175.83333333333334,\n 79.5,\n 17.0,\n 0.0)\n<\/code><\/pre>\n<p>\u0628\u0631\u0627\u06cc \u062a\u062c\u0633\u0645 \u0622\u0646 \u0646\u062a\u0627\u06cc\u062c\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u062e\u0648\u062f \u0631\u0627 \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645 <em>Ks<\/em> \u0647\u0645\u0631\u0627\u0647 \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 WCSS:<\/p>\n<pre><code class=\"hljs\">ks = (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">5<\/span> , <span class=\"hljs-number\">6<\/span> , <span class=\"hljs-number\">7<\/span> , <span class=\"hljs-number\">8<\/span>, <span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">10<\/span>)\nplt.plot(ks, wcss)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-9.png\" alt=\"\" title=\"\"><\/p>\n<p>\u06cc\u06a9 \u0648\u0642\u0641\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u0631\u0648\u06cc \u06cc\u06a9 \u0637\u0631\u062d \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 <code>x = 2<\/code>\u060c \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u067e\u0627\u06cc\u06cc\u0646 \u062f\u0631 \u062e\u0637\u060c \u0648 \u062d\u062a\u06cc \u067e\u0627\u06cc\u06cc\u0646 \u062a\u0631 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 <code>x = 3<\/code>.  \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0645\u0627 \u06cc\u0627\u062f\u0622\u0648\u0631\u06cc \u0645\u06cc \u06a9\u0646\u062f <em>\u0634\u06a9\u0644 \u0622\u0631\u0646\u062c<\/em>.  \u0628\u0627 \u062a\u0631\u0633\u06cc\u0645 Ks \u0628\u0647 \u0647\u0645\u0631\u0627\u0647 WCSS\u060c \u0645\u0627 \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <strong>\u0631\u0648\u0634 \u0622\u0631\u0646\u062c<\/strong> \u0628\u0631\u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u062a\u0639\u062f\u0627\u062f Ks.  \u0648 <em>K \u0627\u0646\u062a\u062e\u0627\u0628 \u0634\u062f\u0647 \u062f\u0642\u06cc\u0642\u0627\u064b \u067e\u0627\u06cc\u06cc\u0646 \u062a\u0631\u06cc\u0646 \u0646\u0642\u0637\u0647 \u0622\u0631\u0646\u062c \u0627\u0633\u062a<\/em>\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0645\u06cc \u0634\u0648\u062f <code>3<\/code> \u0628\u062c\u0627\u06cc <code>2<\/code>\u060c \u062f\u0631 \u0645\u0648\u0631\u062f \u0645\u0627:<\/p>\n<pre><code class=\"hljs\">ks = (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">5<\/span> , <span class=\"hljs-number\">6<\/span> , <span class=\"hljs-number\">7<\/span> , <span class=\"hljs-number\">8<\/span>, <span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">10<\/span>)\nplt.plot(ks, wcss);\nplt.axvline(<span class=\"hljs-number\">3<\/span>, linestyle=<span class=\"hljs-string\">'--'<\/span>, color=<span class=\"hljs-string\">'r'<\/span>)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-10.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062e\u0648\u0634\u0647\u200c\u0627\u06cc K-Means \u0631\u0627 \u062f\u0648\u0628\u0627\u0631\u0647 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0645\u0627 \u0686\u06af\u0648\u0646\u0647 \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc\u200c\u0631\u0633\u0646\u062f <em>\u0633\u0647 \u062e\u0648\u0634\u0647<\/em>:<\/p>\n<pre><code class=\"hljs\">kmeans = KMeans(n_clusters=<span class=\"hljs-number\">3<\/span>, random_state=<span class=\"hljs-number\">42<\/span>)\nkmeans.fit(points)\nsns.scatterplot(x = points(:,<span class=\"hljs-number\">0<\/span>), y = points(:,<span class=\"hljs-number\">1<\/span>), hue=kmeans.labels_)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-11.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0645\u0627 \u0642\u0628\u0644\u0627\u064b \u0627\u0632 \u062f\u0648 \u062e\u0648\u0634\u0647 \u0631\u0627\u0636\u06cc \u0628\u0648\u062f\u06cc\u0645\u060c \u0627\u0645\u0627 \u0637\u0628\u0642 \u0631\u0648\u0634 \u0622\u0631\u0646\u062c\u060c \u0633\u0647 \u062e\u0648\u0634\u0647 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0645\u0627 \u0645\u0646\u0627\u0633\u0628\u200c\u062a\u0631 \u0628\u0648\u062f.  \u062f\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0628\u0647 \u062c\u0627\u06cc \u062f\u0648 \u0641\u0631\u0648\u0634\u06af\u0627\u0647\u060c \u0633\u0647 \u0646\u0648\u0639 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a.  \u0642\u0628\u0644 \u0627\u0632 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0632\u0627\u0646\u0648\u06cc\u06cc \u0628\u0647 \u062e\u0648\u0634\u0647 \u0647\u0627\u06cc \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0647\u0627\u06cc \u062c\u0646\u0648\u0628 \u063a\u0631\u0628\u06cc \u0648 \u0634\u0645\u0627\u0644 \u0634\u0631\u0642\u06cc \u0641\u06a9\u0631 \u0645\u06cc \u06a9\u0631\u062f\u06cc\u0645\u060c \u0627\u06a9\u0646\u0648\u0646 \u062f\u0631 \u0645\u0631\u06a9\u0632 \u0646\u06cc\u0632 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0647\u0627\u06cc\u06cc \u062f\u0627\u0631\u06cc\u0645.  \u0634\u0627\u06cc\u062f \u0627\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0645\u06a9\u0627\u0646 \u062e\u0648\u0628\u06cc \u0628\u0631\u0627\u06cc \u0627\u0641\u062a\u062a\u0627\u062d \u06cc\u06a9 \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u062f\u06cc\u06af\u0631 \u0628\u0627\u0634\u062f \u0632\u06cc\u0631\u0627 \u0631\u0642\u0627\u0628\u062a \u06a9\u0645\u062a\u0631\u06cc \u062f\u0631 \u0622\u0646 \u0646\u0632\u062f\u06cc\u06a9\u06cc \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a.<\/p>\n<h3 id=\"alternativeclusterqualitymeasures\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%db%8c%d8%a7%d8%b1%d9%87%d8%a7%db%8c_%da%a9%db%8c%d9%81%db%8c_%d8%ae%d9%88%d8%b4%d9%87_%d8%a7%db%8c_%d8%ac%d8%a7%db%8c%da%af%d8%b2%db%8c%d9%86\"><\/span>\u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u06a9\u06cc\u0641\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0647\u0646\u06af\u0627\u0645 \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u06a9\u06cc\u0641\u06cc\u062a \u062e\u0648\u0634\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f:<\/p>\n<ul>\n<li><strong>\u0627\u0645\u062a\u06cc\u0627\u0632 \u0633\u06cc\u0644\u0648\u0626\u062a<\/strong> &#8211; \u0646\u0647 \u062a\u0646\u0647\u0627 \u0641\u0627\u0635\u0644\u0647 \u0628\u06cc\u0646 \u0646\u0642\u0627\u0637 \u062f\u0631\u0648\u0646 \u062e\u0648\u0634\u0647 \u0627\u06cc \u0628\u0644\u06a9\u0647 \u0628\u06cc\u0646 \u062e\u0648\u062f \u062e\u0648\u0634\u0647 \u0647\u0627 \u0631\u0627 \u0646\u06cc\u0632 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0645\u06cc \u06a9\u0646\u062f<\/li>\n<li><strong>\u0628\u06cc\u0646 \u062e\u0648\u0634\u0647 \u0647\u0627 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639 \u0647\u0627<\/strong> <strong><em>(BCSS)<\/em><\/strong>  &#8211; \u0645\u062a\u0631\u06cc\u06a9 \u0645\u06a9\u0645\u0644 WCSS<\/li>\n<li><strong>\u062e\u0637\u0627\u06cc \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a<\/strong> <strong><em>(SSE)<\/em><\/strong><\/li>\n<li><strong>\u062d\u062f\u0627\u06a9\u062b\u0631 \u0634\u0639\u0627\u0639<\/strong> &#8211; \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u062a\u0627 \u0645\u0631\u06a9\u0632 \u0622\u0646 \u0631\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0645\u06cc \u06a9\u0646\u062f<\/li>\n<li><strong>\u0634\u0639\u0627\u0639 \u0645\u062a\u0648\u0633\u0637<\/strong> &#8211; \u0645\u062c\u0645\u0648\u0639 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0641\u0627\u0635\u0644\u0647 \u0627\u0632 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u062a\u0627 \u0645\u0631\u06a9\u0632 \u0622\u0646 \u062a\u0642\u0633\u06cc\u0645 \u0628\u0631 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627.<\/li>\n<\/ul>\n<p>\u062a\u0648\u0635\u06cc\u0647 \u0645\u06cc \u0634\u0648\u062f \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\u062f \u0648 \u0628\u0627 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0622\u0646\u0647\u0627 \u0622\u0634\u0646\u0627 \u0634\u0648\u06cc\u062f \u0631\u0648\u06cc \u0645\u0634\u06a9\u0644 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u062e\u06cc \u0627\u0632 \u06af\u0632\u06cc\u0646\u0647 \u0647\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u06a9\u0627\u0631\u0628\u0631\u062f\u06cc \u062a\u0631 \u0627\u0632 \u067e\u0631\u06a9\u0627\u0631\u0628\u0631\u062f\u062a\u0631\u06cc\u0646 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627 \u0628\u0627\u0634\u0646\u062f <em>(\u0646\u0645\u0631\u0647 WCSS \u0648 Silhouette)<\/em>.<\/p>\n<p>\u062f\u0631 \u067e\u0627\u06cc\u0627\u0646\u060c \u0645\u0627\u0646\u0646\u062f \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0639\u0644\u0645 \u062f\u0627\u062f\u0647\u060c \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u062f\u0631\u0648\u0646 \u0647\u0631 \u062e\u0648\u0634\u0647 \u0631\u0627 \u06a9\u0627\u0647\u0634 \u062f\u0647\u06cc\u0645 \u0648 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u0628\u06cc\u0646 \u062e\u0648\u0634\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0631\u0627 \u0628\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0628\u0631\u0633\u0627\u0646\u06cc\u0645.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u0627 \u062e\u0648\u0634\u0647 \u0647\u0627\u06cc \u062a\u0639\u0631\u06cc\u0641 \u0634\u062f\u0647 \u0648 \u0642\u0627\u0628\u0644 \u062a\u0641\u06a9\u06cc\u06a9 \u0628\u06cc\u0634\u062a\u0631\u06cc \u062f\u0627\u0631\u06cc\u0645.<\/p>\n<h2 id=\"applyingkmeansonanotherdataset\"><span class=\"ez-toc-section\" id=\"%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_k-means_%d8%b1%d9%88%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_%d8%af%db%8c%da%af%d8%b1\"><\/span>\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 K-Means \u0631\u0648\u06cc \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062f\u06cc\u06af\u0631<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u0632 \u0622\u0645\u0648\u062e\u062a\u0647 \u0647\u0627\u06cc \u062e\u0648\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062f\u06cc\u06af\u0631\u06cc  \u0627\u06cc\u0646 \u0628\u0627\u0631 \u0633\u0639\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc\u06cc \u0627\u0632 \u0634\u0631\u0627\u0628 \u0647\u0627\u06cc \u0645\u0634\u0627\u0628\u0647 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645.<\/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> \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u062f\u0627\u0646\u0644\u0648\u062f \u06a9\u0646\u06cc\u062f <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/gist.githubusercontent.com\/DavidLandup0\/02071b3468e2e32461ca92263359fc91\/raw\/e6aa0cabb7ce1ad5c93c854444705264bfcbf92a\/Wine%2520Clustering\">\u0627\u06cc\u0646\u062c\u0627<\/a>.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0645\u0627 \u0628\u0627 \u0648\u0627\u0631\u062f\u0627\u062a \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>pandas<\/code> \u0628\u0631\u0627\u06cc \u062e\u0648\u0627\u0646\u062f\u0646 <code>wine-clustering<\/code> CSV <em>(\u0645\u0642\u0627\u062f\u06cc\u0631 \u062c\u062f\u0627 \u0634\u062f\u0647 \u0628\u0627 \u06a9\u0627\u0645\u0627)<\/em> \u0641\u0627\u06cc\u0644 \u0628\u0647 a <code>Dataframe<\/code> \u0633\u0627\u062e\u062a\u0627\u0631:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> pandas <span class=\"hljs-keyword\">as<\/span> pd\n\ndf = pd.read_csv(<span class=\"hljs-string\">'wine-clustering.csv'<\/span>)\n<\/code><\/pre>\n<p>\u067e\u0633 \u0627\u0632 \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc \u0622\u0646\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u067e\u0646\u062c \u0631\u06a9\u0648\u0631\u062f \u0627\u0648\u0644 \u062f\u0627\u062f\u0647 \u0628\u0627 \u0622\u0646 \u0628\u06cc\u0627\u0646\u062f\u0627\u0632\u06cc\u0645 <code>head()<\/code> \u0631\u0648\u0634:<\/p>\n<pre><code class=\"hljs\">df.head()\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u062f\u0631:<\/p>\n<pre><code class=\"hljs\">    Alcohol \tMalic_Acid \tAsh \tAsh_Alcanity \tMagnesium \tTotal_Phenols \tFlavonoids \tNonflavanoid_Phenols \tProanthocyanidins \tColor_Intensity \tHue \tOD280 \tProline\n0 \t14.23 \t\t1.71 \t\t2.43 \t15.6 \t\t\t127 \t\t2.80 \t\t\t3.06 \t\t0.28 \t\t\t\t\t2.29 \t\t\t\t5.64 \t\t\t\t1.04 \t3.92 \t1065\n1 \t13.20 \t\t1.78 \t\t2.14 \t11.2 \t\t\t100 \t\t2.65 \t\t\t2.76 \t\t0.26 \t\t\t\t\t1.28 \t\t\t\t4.38 \t\t\t\t1.05 \t3.40 \t1050\n2 \t13.16 \t\t2.36 \t\t2.67 \t18.6 \t\t\t101 \t\t2.80 \t\t\t3.24 \t\t0.30 \t\t\t\t\t2.81 \t\t\t\t5.68 \t\t\t\t1.03 \t3.17 \t1185\n3 \t14.37 \t\t1.95 \t\t2.50 \t16.8 \t\t\t113 \t\t3.85 \t\t\t3.49 \t\t0.24 \t\t\t\t\t2.18 \t\t\t\t7.80 \t\t\t\t0.86 \t3.45 \t1480\n4 \t13.24 \t\t2.59 \t\t2.87 \t21.0 \t\t\t118 \t\t2.80 \t\t\t2.69 \t\t0.39 \t\t\t\t\t1.82 \t\t\t\t4.32 \t\t\t\t1.04 \t2.93 \t735\n<\/code><\/pre>\n<p>\u0645\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0627\u0632 \u0645\u0648\u0627\u062f \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0634\u0631\u0627\u0628 \u0647\u0627 \u062f\u0627\u0631\u06cc\u0645.  \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627\u060c \u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0633\u062a\u0648\u0646 \u0647\u0627\u06cc \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0646\u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a \u0632\u06cc\u0631\u0627 \u0647\u0645\u0647 \u0622\u0646\u0647\u0627 \u0639\u062f\u062f\u06cc \u0647\u0633\u062a\u0646\u062f.  \u062d\u0627\u0644 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0622\u0645\u0627\u0631 \u062a\u0648\u0635\u06cc\u0641\u06cc \u0628\u0627 <code>describe()<\/code> \u0631\u0648\u0634:<\/p>\n<pre><code class=\"hljs\">df.describe().T \n<\/code><\/pre>\n<p>\u062c\u062f\u0648\u0644 \u062a\u0648\u0635\u06cc\u0641:<\/p>\n<pre><code class=\"hljs\">                         count \tmean \t\tstd \t\tmin \t25% \t50% \t75% \t\tmax\nAlcohol \t\t\t\t178.0 \t13.000618 \t0.811827 \t11.03 \t12.3625 13.050 \t13.6775 \t14.83\nMalic_Acid \t\t\t\t178.0 \t2.336348 \t1.117146 \t0.74 \t1.6025 \t1.865 \t3.0825 \t\t5.80\nAsh \t\t\t\t\t178.0 \t2.366517 \t0.274344 \t1.36 \t2.2100 \t2.360 \t2.5575 \t\t3.23\nAsh_Alcanity \t\t\t178.0 \t19.494944 \t3.339564 \t10.60 \t17.2000 19.500 \t21.5000 \t30.00\nMagnesium \t\t\t\t178.0 \t99.741573 \t14.282484 \t70.00 \t88.0000 98.000 \t107.0000 \t162.00\nTotal_Phenols \t\t\t178.0 \t2.295112 \t0.625851 \t0.98 \t1.7425 \t2.355 \t2.8000 \t\t3.88\nFlavonoids \t\t\t\t178.0 \t2.029270 \t0.998859 \t0.34 \t1.2050 \t2.135 \t2.8750 \t\t5.08\nNonflavanoid_Phenols \t178.0 \t0.361854 \t0.124453 \t0.13 \t0.2700 \t0.340 \t0.4375 \t\t0.66\nProanthocyanidins \t\t178.0 \t1.590899 \t0.572359 \t0.41 \t1.2500 \t1.555 \t1.9500 \t\t3.58\nColor_Intensity \t\t178.0 \t5.058090 \t2.318286 \t1.28 \t3.2200 \t4.690 \t6.2000 \t\t13.00\nHue \t\t\t\t\t178.0 \t0.957449 \t0.228572 \t0.48 \t0.7825 \t0.965 \t1.1200 \t\t1.71\nOD280 \t\t\t\t\t178.0 \t2.611685 \t0.709990 \t1.27 \t1.9375 \t2.780 \t3.1700 \t\t4.00\nProline \t\t\t\t178.0 \t746.893258 \t314.907474 \t278.00 \t500.500 673.500 985.0000 \t1680.00\n<\/code><\/pre>\n<p>\u0628\u0627 \u0646\u06af\u0627\u0647 \u06a9\u0631\u062f\u0646 \u0628\u0647 \u062c\u062f\u0648\u0644 \u0645\u0634\u062e\u0635 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0645\u0642\u062f\u0627\u0631\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f <em>\u062a\u0646\u0648\u0639 \u062f\u0631 \u062f\u0627\u062f\u0647 \u0647\u0627<\/em> &#8211; \u0628\u0631\u0627\u06cc \u0628\u0631\u062e\u06cc \u0627\u0632 \u0633\u062a\u0648\u0646 \u0647\u0627 \u0645\u0627\u0646\u0646\u062f <code>Alcohol<\/code> \u0628\u06cc\u0634\u062a\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0648 \u0628\u0631\u0627\u06cc \u062f\u06cc\u06af\u0631\u0627\u0646\u060c \u0645\u0627\u0646\u0646\u062f <code>Malic_Acid<\/code>\u060c \u06a9\u0645\u062a\u0631  \u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631 <code>null<\/code>\u060c \u06cc\u0627 <code>NaN<\/code> \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0645\u0627:<\/p>\n<pre><code class=\"hljs\">df.info()\n<\/code><\/pre>\n<pre><code class=\"hljs\">&lt;class 'pandas.core.frame.DataFrame'&gt;\nRangeIndex: 178 entries, 0 to 177\nData columns (total 13 columns):\n #   Column                Non-Null Count  Dtype  \n---  ------                --------------  -----  \n 0   Alcohol               178 non-null    float64\n 1   Malic_Acid            178 non-null    float64\n 2   Ash                   178 non-null    float64\n 3   Ash_Alcanity          178 non-null    float64\n 4   Magnesium             178 non-null    int64  \n 5   Total_Phenols         178 non-null    float64\n 6   Flavonoids            178 non-null    float64\n 7   Nonflavanoid_Phenols  178 non-null    float64\n 8   Proanthocyanidins       178 non-null    float64\n 9   Color_Intensity       178 non-null    float64\n 10  Hue                   178 non-null    float64\n 11  OD280                 178 non-null    float64\n 12  Proline               178 non-null    int64  \ndtypes: float64(11), int64(2)\nmemory usage: 18.2 KB\n<\/code><\/pre>\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646\u06a9\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062e\u0627\u0644\u06cc \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f\u060c \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u062d\u0630\u0641 \u06cc\u0627 \u0648\u0627\u0631\u062f \u06a9\u0631\u062f\u0646 \u062f\u0627\u062f\u0647 \u0646\u06cc\u0633\u062a.  \u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 Seaborn \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 <code>pairplot()<\/code> \u0628\u0631\u0627\u06cc \u0645\u0634\u0627\u0647\u062f\u0647 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0648 \u0628\u0631\u0631\u0633\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0622\u06cc\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062c\u0641\u062a \u0633\u062a\u0648\u0646 \u0647\u0627\u06cc\u06cc \u0631\u0627 \u062a\u0634\u06a9\u06cc\u0644 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0628\u0631\u0627\u06cc \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u062c\u0627\u0644\u0628 \u0628\u0627\u0634\u0646\u062f:<\/p>\n<pre><code class=\"hljs\">sns.pairplot(df)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-12.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0628\u0627 \u0646\u06af\u0627\u0647 \u06a9\u0631\u062f\u0646 \u0628\u0647 \u0646\u0645\u0648\u062f\u0627\u0631 \u062c\u0641\u062a\u060c \u062f\u0648 \u0633\u062a\u0648\u0646 \u0628\u0631\u0627\u06cc \u0627\u0647\u062f\u0627\u0641 \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0627\u0645\u06cc\u062f\u0648\u0627\u0631\u06a9\u0646\u0646\u062f\u0647 \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc\u200c\u0631\u0633\u0646\u062f &#8211; <code>Alcohol<\/code> \u0648 <code>OD280<\/code> (\u06a9\u0647 \u0631\u0648\u0634\u06cc \u0628\u0631\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u063a\u0644\u0638\u062a \u067e\u0631\u0648\u062a\u0626\u06cc\u0646 \u062f\u0631 \u0634\u0631\u0627\u0628 \u0647\u0627 \u0627\u0633\u062a).  \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u06a9\u0647 3 \u062e\u0648\u0634\u0647 \u0645\u062c\u0632\u0627 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u0631\u0648\u06cc \u0637\u0631\u062d \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0648 \u062a\u0627 \u0627\u0632 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0627 \u0647\u0645 \u062a\u0631\u06a9\u06cc\u0628 \u0645\u06cc \u06a9\u0646\u0646\u062f.<\/p>\n<p>\u0633\u062a\u0648\u0646 \u0647\u0627\u06cc \u062f\u06cc\u06af\u0631\u06cc \u0646\u06cc\u0632 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u0646\u062f \u06a9\u0647 \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u062f\u0627\u0631\u0646\u062f.  \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u062a\u0631\u06cc\u0646 <code>Alcohol<\/code> \u0648 <code>Total_Phenols<\/code>\u060c \u0648 <code>Alcohol<\/code> \u0648 <code>Flavonoids<\/code>.  \u0622\u0646\u0647\u0627 \u0631\u0648\u0627\u0628\u0637 \u062e\u0637\u06cc \u0628\u0633\u06cc\u0627\u0631 \u062e\u0648\u0628\u06cc \u062f\u0627\u0631\u0646\u062f \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631 \u062c\u0641\u062a \u0645\u0634\u0627\u0647\u062f\u0647 \u06a9\u0631\u062f.<\/p>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u062a\u0645\u0631\u06a9\u0632 \u0645\u0627 \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0628\u0627 K-Means \u0627\u0633\u062a\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0645\u062b\u0644\u0627\u064b \u06cc\u06a9 \u062c\u0641\u062a \u0633\u062a\u0648\u0646 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u0645 <code>Alcohol<\/code> \u0648 <code>OD280<\/code>\u0648 \u0631\u0648\u0634 elbow \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\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> \u0647\u0646\u06af\u0627\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0633\u062a\u0648\u0646 \u0647\u0627\u06cc \u0628\u06cc\u0634\u062a\u0631\u06cc \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647\u060c \u0646\u06cc\u0627\u0632 \u0628\u0647 \u062a\u0631\u0633\u06cc\u0645 \u0646\u0645\u0648\u062f\u0627\u0631 \u062f\u0631 3 \u0628\u0639\u062f \u06cc\u0627 \u06a9\u0627\u0647\u0634 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0628\u0647 \u0627\u062c\u0632\u0627\u06cc \u0627\u0635\u0644\u06cc (\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 PCA) \u0648\u062c\u0648\u062f \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a.  \u0627\u06cc\u0646 \u06cc\u06a9 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0645\u0639\u062a\u0628\u0631 \u0648 \u0631\u0627\u06cc\u062c \u062a\u0631 \u0627\u0633\u062a\u060c \u0641\u0642\u0637 \u0645\u0637\u0645\u0626\u0646 \u0634\u0648\u06cc\u062f \u06a9\u0647 \u0627\u062c\u0632\u0627\u06cc \u0627\u0635\u0644\u06cc \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u062f \u0631\u0648\u06cc \u0686\u0642\u062f\u0631 \u0622\u0646\u0647\u0627 \u062a\u0648\u0636\u06cc\u062d \u0645\u06cc \u062f\u0647\u0646\u062f \u0648 \u062f\u0631 \u0646\u0638\u0631 \u062f\u0627\u0631\u0646\u062f \u06a9\u0647 \u0647\u0646\u06af\u0627\u0645 \u06a9\u0627\u0647\u0634 \u0627\u0628\u0639\u0627\u062f \u062f\u0627\u062f\u0647\u060c \u0645\u0642\u062f\u0627\u0631\u06cc \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0627\u0632 \u062f\u0633\u062a \u0645\u06cc \u0631\u0648\u062f &#8211; \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0637\u0631\u062d \u06cc\u06a9 <strong>\u062a\u0642\u0631\u06cc\u0628<\/strong> \u0627\u0632 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc\u060c \u0646\u0647 \u0627\u06cc\u0646\u06a9\u0647 \u0648\u0627\u0642\u0639\u0627 \u0686\u06af\u0648\u0646\u0647 \u0627\u0633\u062a.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u0645\u0648\u062f\u0627\u0631 \u067e\u0631\u0627\u06a9\u0646\u062f\u06af\u06cc \u0631\u0627 \u0628\u0627 \u0622\u0646 \u062f\u0648 \u0633\u062a\u0648\u0646 \u06a9\u0647 \u0645\u062d\u0648\u0631 \u0622\u0646 \u062a\u0646\u0638\u06cc\u0645 \u0634\u062f\u0647 \u0627\u0633\u062a \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0646\u0642\u0627\u0637\u06cc \u0631\u0627 \u06a9\u0647 \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u0628\u0647 \u06af\u0631\u0648\u0647\u200c\u0647\u0627 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0646\u06cc\u0645\u060c \u0646\u06af\u0627\u0647 \u062f\u0642\u06cc\u0642\u200c\u062a\u0631\u06cc \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">sns.scatterplot(data=df, x=<span class=\"hljs-string\">'OD280'<\/span>, y=<span class=\"hljs-string\">'Alcohol'<\/span>)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-13.png\" alt=\"\" title=\"\"><\/p>\n<p>\u062d\u0627\u0644\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0633\u062a\u0648\u0646\u200c\u0647\u0627\u06cc\u0645\u0627\u0646 \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645 \u0648 \u0627\u0632 \u0631\u0648\u0634 elbow \u0628\u0631\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647\u200c\u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645.  \u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0628\u0627 \u0634\u0631\u0648\u0639 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <code>kmeans++<\/code>  \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0627\u0632 \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u0633\u0631\u06cc\u0639\u062a\u0631:<\/p>\n<pre><code class=\"hljs\">values = df((<span class=\"hljs-string\">'OD280'<\/span>, <span class=\"hljs-string\">'Alcohol'<\/span>))\n\nwcss_wine = () \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\">1<\/span>, <span class=\"hljs-number\">11<\/span>): \n    kmeans = KMeans(n_clusters = i, init = <span class=\"hljs-string\">'k-means++'<\/span>, random_state = <span class=\"hljs-number\">42<\/span>)\n    kmeans.fit(values) \n    wcss_wine.append(kmeans.inertia_)\n<\/code><\/pre>\n<p>\u0645\u0627 WCSS \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0646\u062a\u0627\u06cc\u062c \u0631\u0627 \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">clusters_wine = (<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">6<\/span>, <span class=\"hljs-number\">7<\/span>, <span class=\"hljs-number\">8<\/span>, <span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">10<\/span>)\nplt.plot(clusters_wine, wcss_wine)\nplt.axvline(<span class=\"hljs-number\">3<\/span>, linestyle=<span class=\"hljs-string\">'--'<\/span>, color=<span class=\"hljs-string\">'r'<\/span>)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-14.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0637\u0628\u0642 \u0631\u0648\u0634 \u0622\u0631\u0646\u062c \u0628\u0627\u06cc\u062f 3 \u062e\u0648\u0634\u0647 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645.  \u0628\u0631\u0627\u06cc \u0645\u0631\u062d\u0644\u0647 \u0622\u062e\u0631\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0646\u0642\u0627\u0637 \u062e\u0648\u062f \u0631\u0627 \u0628\u0647 3 \u062e\u0648\u0634\u0647 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0622\u0646 \u062f\u0633\u062a\u0647 \u0627\u0632 \u062e\u0648\u0634\u0647 \u0647\u0627\u06cc \u0645\u0634\u062e\u0635 \u0634\u062f\u0647 \u0628\u0627 \u0631\u0646\u06af \u0647\u0627 \u0631\u0627 \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">kmeans_wine = KMeans(n_clusters=<span class=\"hljs-number\">3<\/span>, random_state=<span class=\"hljs-number\">42<\/span>)\nkmeans_wine.fit(values)\nsns.scatterplot(x = values(<span class=\"hljs-string\">'OD280'<\/span>), y = values(<span class=\"hljs-string\">'Alcohol'<\/span>), hue=kmeans_wine.labels_)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/guide-to-k-means-clustering-with-scikit-lear-15.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062e\u0648\u0634\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 <code>0<\/code>\u060c <code>1<\/code>\u060c \u0648 <code>2<\/code> \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631  \u0645\u0633\u062a\u0642\u0631 \u0631\u0648\u06cc \u062a\u062d\u0644\u06cc\u0644 \u0645\u0627\u060c <em>\u06af\u0631\u0648\u0647 0<\/em> \u062f\u0627\u0631\u0627\u06cc \u0634\u0631\u0627\u0628 \u0647\u0627\u06cc\u06cc \u0628\u0627 \u0645\u062d\u062a\u0648\u0627\u06cc \u067e\u0631\u0648\u062a\u0626\u06cc\u0646 \u0628\u0627\u0644\u0627\u062a\u0631 \u0648 \u0627\u0644\u06a9\u0644 \u06a9\u0645\u062a\u0631\u060c <em>\u06af\u0631\u0648\u0647 1<\/em> \u062f\u0627\u0631\u0627\u06cc \u0634\u0631\u0627\u0628 \u0647\u0627\u06cc\u06cc \u0628\u0627 \u0645\u062d\u062a\u0648\u0627\u06cc \u0627\u0644\u06a9\u0644 \u0628\u0627\u0644\u0627\u062a\u0631 \u0648 \u067e\u0631\u0648\u062a\u0626\u06cc\u0646 \u06a9\u0645\u060c \u0648 <em>\u06af\u0631\u0648\u0647 2<\/em> \u0647\u0645 \u067e\u0631\u0648\u062a\u0626\u06cc\u0646 \u0628\u0627\u0644\u0627 \u0648 \u0647\u0645 \u0627\u0644\u06a9\u0644 \u0628\u0627\u0644\u0627 \u062f\u0631 \u0634\u0631\u0627\u0628 \u0647\u0627\u06cc \u062e\u0648\u062f \u062f\u0627\u0631\u062f.<\/p>\n<p>\u0627\u06cc\u0646 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0628\u0633\u06cc\u0627\u0631 \u062c\u0627\u0644\u0628\u06cc \u0627\u0633\u062a \u0648 \u0645\u0646 \u0634\u0645\u0627 \u0631\u0627 \u062a\u0634\u0648\u06cc\u0642 \u0645\u06cc\u200c\u06a9\u0646\u0645 \u062a\u0627 \u0628\u0627 \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u067e\u0633 \u0627\u0632 \u0639\u0627\u062f\u06cc\u200c\u0633\u0627\u0632\u06cc \u0648 PCA &#8211; \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0627 \u062a\u0641\u0633\u06cc\u0631 \u0646\u062a\u0627\u06cc\u062c \u0648 \u06cc\u0627\u0641\u062a\u0646 \u0627\u062a\u0635\u0627\u0644\u0627\u062a \u062c\u062f\u06cc\u062f\u060c \u0628\u0647 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0628\u06cc\u0634\u062a\u0631 \u0628\u0631\u0648\u06cc\u062f.<\/p>\n<h2 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><em>K-Means<\/em> \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646\u06cc \u0633\u0627\u062f\u0647 \u0648 \u062f\u0631 \u0639\u06cc\u0646 \u062d\u0627\u0644 \u0628\u0633\u06cc\u0627\u0631 \u0645\u0624\u062b\u0631 \u0628\u0631\u0627\u06cc \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u062f\u0627\u062f\u0647 \u0627\u0633\u062a.  \u0628\u0631 \u0627\u0633\u0627\u0633 \u062f\u0627\u062f\u0647 \u0647\u0627 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u0641\u0627\u0635\u0644\u0647 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0628\u06cc\u0646 \u0646\u0642\u0627\u0637 \u062f\u0627\u062f\u0647  \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc K-Means \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0628\u0631\u0627\u06cc \u06af\u0631\u0648\u0647 \u0628\u0646\u062f\u06cc \u0627\u0633\u0646\u0627\u062f \u0645\u062a\u0646\u06cc\u060c \u062a\u0635\u0627\u0648\u06cc\u0631\u060c \u0648\u06cc\u062f\u0626\u0648\u0647\u0627 \u0648 \u0645\u0648\u0627\u0631\u062f \u062f\u06cc\u06af\u0631 \u062f\u0627\u0631\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 1403-01-04 20:05:05<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;14319&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;\u0631\u0627\u0647\u0646\u0645\u0627\u06cc \u0642\u0637\u0639\u06cc \u0628\u0631\u0627\u06cc K-Means Clustering \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\"> 17<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc K-\u0628\u0647 \u0645\u0639\u0646\u06cc \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0627\u0633\u062a \u06cc\u06a9\u06cc \u0627\u0632 \u067e\u0631\u06a9\u0627\u0631\u0628\u0631\u062f\u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646\u06cc \u0628\u062f\u0648\u0646 \u0646\u0638\u0627\u0631\u062a \u0627\u0633\u062a \u06a9\u0647 \u062e\u0648\u0634\u0647\u200c\u0647\u0627\u06cc\u06cc \u0627\u0632 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0631\u0627 \u062a\u0634\u06a9\u06cc\u0644 \u0645\u06cc\u200c\u062f\u0647\u062f. \u0631\u0648\u06cc \u0634\u0628\u0627\u0647\u062a \u0628\u06cc\u0646 \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627\u060c \u0627\u0628\u062a\u062f\u0627 \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0633\u0627\u062f\u0647 \u0645\u06cc \u0627\u0646\u062f\u0627\u0632\u06cc\u0645 \u062a\u0627 \u0628\u0641\u0647\u0645\u06cc\u0645 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 K-Means \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f \u0642\u0628\u0644 \u0627\u0632 \u0627\u062c\u0631\u0627\u06cc \u0622\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn. [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":14320,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[],"class_list":["post-14319","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\/14319","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=14319"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/14319\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/14320"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=14319"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=14319"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=14319"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}