{"id":1245,"date":"2023-07-27T03:54:17","date_gmt":"2023-07-27T03:54:17","guid":{"rendered":"https:\/\/statorials.org\/hi\/%e0%a4%86%e0%a4%b0-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ae%e0%a5%87%e0%a4%a1%e0%a5%8b%e0%a4%87%e0%a4%a1%e0%a5%8d%e0%a4%b8\/"},"modified":"2023-07-27T03:54:17","modified_gmt":"2023-07-27T03:54:17","slug":"%e0%a4%86%e0%a4%b0-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ae%e0%a5%87%e0%a4%a1%e0%a5%8b%e0%a4%87%e0%a4%a1%e0%a5%8d%e0%a4%b8","status":"publish","type":"post","link":"https:\/\/statorials.org\/hi\/%e0%a4%86%e0%a4%b0-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ae%e0%a5%87%e0%a4%a1%e0%a5%8b%e0%a4%87%e0%a4%a1%e0%a5%8d%e0%a4%b8\/","title":{"rendered":"\u0906\u0930 \u092e\u0947\u0902 \u0915\u0947-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938: \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u0909\u0926\u093e\u0939\u0930\u0923"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u090f\u0915 \u092e\u0936\u0940\u0928 \u0932\u0930\u094d\u0928\u093f\u0902\u0917 \u0924\u0915\u0928\u0940\u0915 \u0939\u0948 \u091c\u094b \u0921\u0947\u091f\u093e \u0938\u0947\u091f \u0915\u0947 \u092d\u0940\u0924\u0930 \u0938\u092e\u0942\u0939\u094b\u0902 \u092f\u093e <a href=\"https:\/\/statorials.org\/hi\/\u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940-\u092e\u0947\u0902-\u0905\u0935\u0932\u094b\u0915\u0928\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0905\u0935\u0932\u094b\u0915\u0928\u094b\u0902<\/a> \u0915\u0947 <em>\u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u094b<\/em> \u0916\u094b\u091c\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0932\u0915\u094d\u0937\u094d\u092f \u0910\u0938\u0947 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u094b \u0922\u0942\u0902\u0922\u0928\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0905\u0935\u0932\u094b\u0915\u0928 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0902, \u091c\u092c\u0915\u093f \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u092e\u0942\u0939\u094b\u0902 \u092e\u0947\u0902 \u0905\u0935\u0932\u094b\u0915\u0928 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0938\u0947 \u0915\u093e\u092b\u0940 \u092d\u093f\u0928\u094d\u0928 \u0939\u094b\u0902\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 <a href=\"https:\/\/statorials.org\/hi\/\u092a\u0930\u094d\u092f\u0935\u0947\u0915\u094d\u0937\u093f\u0924-\u092c\u0928\u093e\u092e-\u0905\u092a\u0930\u094d\u092f\u0935\u0947\u0915\u094d\u0937\u093f\u0924-\u0936\u093f\u0915\u094d\u0937\u0923\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u092c\u093f\u0928\u093e \u092a\u0930\u094d\u092f\u0935\u0947\u0915\u094d\u0937\u093f\u0924 \u0936\u093f\u0915\u094d\u0937\u0923<\/a> \u0915\u093e \u090f\u0915 \u0930\u0942\u092a \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0939\u092e \u0915\u0947\u0935\u0932 <a href=\"https:\/\/statorials.org\/hi\/\u091a\u0930-\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915-\u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930<\/a> \u0915\u0947 \u092e\u0942\u0932\u094d\u092f \u0915\u0940 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u093e\u0923\u0940 \u0915\u0930\u0928\u0947 \u0915\u0947 \u092c\u091c\u093e\u092f \u0921\u0947\u091f\u093e \u0938\u0947\u091f \u0915\u0947 \u092d\u0940\u0924\u0930 \u0938\u0902\u0930\u091a\u0928\u093e \u0916\u094b\u091c\u0928\u0947 \u0915\u0940 \u0915\u094b\u0936\u093f\u0936 \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0905\u0915\u094d\u0938\u0930 \u0935\u093f\u092a\u0923\u0928 \u092e\u0947\u0902 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0935\u094d\u092f\u0935\u0938\u093e\u092f\u094b\u0902 \u0915\u0947 \u092a\u093e\u0938 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0924\u0915 \u092a\u0939\u0941\u0902\u091a \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u0948\u0938\u0947:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0918\u0930\u0947\u0932\u0942 \u0906\u092f<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u092a\u0930\u093f\u0935\u093e\u0930 \u0915\u093e \u0906\u0915\u093e\u0930<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0918\u0930 \u0915\u0947 \u092e\u0941\u0916\u093f\u092f\u093e \u0915\u093e \u092a\u0947\u0936\u093e<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0928\u093f\u0915\u091f\u0924\u092e \u0936\u0939\u0930\u0940 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0938\u0947 \u0926\u0942\u0930\u0940<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u091c\u092c \u092f\u0939 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0924\u094b \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0909\u0928 \u0918\u0930\u094b\u0902 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u094b \u0938\u092e\u093e\u0928 \u0939\u0948\u0902 \u0914\u0930 \u0915\u0941\u091b \u0909\u0924\u094d\u092a\u093e\u0926\u094b\u0902 \u0915\u094b \u0916\u0930\u0940\u0926\u0928\u0947 \u092f\u093e \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0935\u093f\u091c\u094d\u091e\u093e\u092a\u0928 \u092a\u0930 \u092c\u0947\u0939\u0924\u0930 \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u0926\u0947\u0928\u0947 \u0915\u0940 \u0905\u0927\u093f\u0915 \u0938\u0902\u092d\u093e\u0935\u0928\u093e \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u0947 \u0938\u092c\u0938\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0915\u094b <a href=\"https:\/\/statorials.org\/hi\/k-\u0915\u093e-\u0905\u0930\u094d\u0925-\u0939\u0948-r-\u092e\u0947\u0902-\u0938\u092e\u0942\u0939-\u092c\u0928\u093e\u0928\u093e\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0915\u0947-\u092e\u0940\u0928\u094d\u0938 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u0947<\/a> \u0930\u0942\u092a \u092e\u0947\u0902 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0926\u0941\u0930\u094d\u092d\u093e\u0917\u094d\u092f \u0938\u0947, \u092f\u0939 \u0935\u093f\u0927\u093f \u0906\u0909\u091f\u0932\u0947\u0930\u094d\u0938 \u0938\u0947 \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948, \u092f\u0939\u0940 \u0915\u093e\u0930\u0923 \u0939\u0948 \u0915\u093f \u0905\u0915\u094d\u0938\u0930 \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u093e \u0935\u093f\u0915\u0932\u094d\u092a <strong>\u0915\u0947-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917<\/strong> \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>K-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u094d\u092f\u093e \u0939\u0948?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">K-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u090f\u0915 \u0910\u0938\u0940 \u0924\u0915\u0928\u0940\u0915 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0939\u092e \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u094b \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092e\u0947\u0902 <em>K<\/em> \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u092e\u0947\u0902 \u0930\u0916\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0905\u0902\u0924\u093f\u092e \u0932\u0915\u094d\u0937\u094d\u092f <em>K<\/em> \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u092c\u0928\u093e\u0928\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0905\u0935\u0932\u094b\u0915\u0928 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u091c\u092c\u0915\u093f \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u092e\u0942\u0939\u094b\u0902 \u092e\u0947\u0902 \u0905\u0935\u0932\u094b\u0915\u0928 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0938\u0947 \u0915\u093e\u092b\u0940 \u092d\u093f\u0928\u094d\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u092e\u0947\u0902, \u0939\u092e K-\u092e\u0940\u0928\u094d\u0938 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091a\u0930\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. <em>K<\/em> \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u092e\u093e\u0928 \u091a\u0941\u0928\u0947\u0902.<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947, \u0939\u092e\u0947\u0902 \u092f\u0939 \u0924\u092f \u0915\u0930\u0928\u093e \u0939\u094b\u0917\u093e \u0915\u093f \u0939\u092e \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u0947 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0905\u0915\u094d\u0938\u0930 \u0939\u092e\u0947\u0902 <em>K<\/em> \u0915\u0947 \u0932\u093f\u090f \u0915\u0908 \u0905\u0932\u0917-\u0905\u0932\u0917 \u092e\u093e\u0928\u094b\u0902 \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0928\u0947 \u0914\u0930 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948 \u0924\u093e\u0915\u093f \u092f\u0939 \u0926\u0947\u0916\u093e \u091c\u093e \u0938\u0915\u0947 \u0915\u093f \u0915\u093f\u0938\u0940 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \u0915\u094c\u0928 \u0938\u0947 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915 \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0932\u0917\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. 1 \u0938\u0947 <em>K<\/em> \u0924\u0915, \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u094b \u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u092e\u0947\u0902 \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0915\u0930\u0947\u0902\u0964<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0924\u092c \u0924\u0915 \u0915\u0930\u0947\u0902 \u091c\u092c \u0924\u0915 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0905\u0938\u093e\u0907\u0928\u092e\u0947\u0902\u091f \u092c\u0926\u0932\u0928\u093e \u092c\u0902\u0926 \u0928 \u0939\u094b \u091c\u093e\u090f\u0964<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <em>K<\/em> \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0915\u0947 \u0932\u093f\u090f, <em>\u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0915\u0947 \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0915\u0947 \u0915\u0947\u0902\u0926\u094d\u0930 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902\u0964<\/em> \u092f\u0939 <em>k<\/em> \u0935\u0947\u0902 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0915\u0947 \u0905\u0935\u0932\u094b\u0915\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u0941\u0935\u093f\u0927\u093e\u0913\u0902 \u0915\u0947 <em>\u092a\u0940<\/em> <b>\u092e\u093e\u0927\u094d\u092f\u0915\u094b\u0902<\/b> \u0915\u093e \u0935\u0947\u0915\u094d\u091f\u0930 \u0939\u0948\u0964<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u094b \u0928\u093f\u0915\u091f\u0924\u092e \u0915\u0947\u0928\u094d\u0926\u094d\u0930\u0915 \u0935\u093e\u0932\u0947 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u092e\u0947\u0902 \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0915\u0930\u0947\u0902\u0964 \u092f\u0939\u093e\u0902, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Euclidean_distance#Squared_Euclidean_distance\" target=\"_blank\" rel=\"noopener noreferrer\">\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u093f\u092f\u0928 \u0926\u0942\u0930\u0940 \u0915\u093e<\/a> \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 <em>\u0928\u093f\u0915\u091f\u0924\u092e \u0915\u094b<\/em> \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/span><\/li>\n<\/ul>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>\u0924\u0915\u0928\u0940\u0915\u0940 \u0928\u094b\u091f:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u091a\u0942\u0901\u0915\u093f k-medoids \u0938\u093e\u0927\u0928\u094b\u0902 \u0915\u0947 \u092c\u091c\u093e\u092f \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0938\u0947\u0902\u091f\u094d\u0930\u094b\u0907\u0921\u094d\u0938 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0924\u093e \u0939\u0948, \u092f\u0939 k-\u092e\u0940\u0928\u094d\u0938 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0906\u0909\u091f\u0932\u0947\u0930\u094d\u0938 \u0915\u0947 \u0932\u093f\u090f \u0905\u0927\u093f\u0915 \u092e\u091c\u092c\u0942\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u092e\u0947\u0902, \u092f\u0926\u093f \u0921\u0947\u091f\u093e \u0938\u0947\u091f \u092e\u0947\u0902 \u0915\u094b\u0908 \u091a\u0930\u092e \u0906\u0909\u091f\u0932\u0947\u0930 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902, \u0924\u094b \u0915\u0947-\u092e\u0940\u0928\u094d\u0938 \u0914\u0930 \u0915\u0947-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0938\u092e\u093e\u0928 \u092a\u0930\u093f\u0923\u093e\u092e \u0926\u0947\u0902\u0917\u0947\u0964<\/span><\/p>\n<\/blockquote>\n<h3> <span style=\"color: #000000;\"><strong>\u0906\u0930 \u092e\u0947\u0902 \u0915\u0947-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 \u0906\u0930 \u092e\u0947\u0902 \u0915\u0947-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902 \u0907\u0938\u0915\u093e \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u0909\u0926\u093e\u0939\u0930\u0923 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u091a\u0930\u0923 1: \u0906\u0935\u0936\u094d\u092f\u0915 \u092a\u0948\u0915\u0947\u091c \u0932\u094b\u0921 \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947, \u0939\u092e \u0906\u0930 \u092e\u0947\u0902 \u0915\u0947-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u0947 \u0932\u093f\u090f \u0915\u0908 \u0909\u092a\u092f\u094b\u0917\u0940 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0935\u093e\u0932\u0947 \u0926\u094b \u092a\u0948\u0915\u0947\u091c \u0932\u094b\u0921 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #993300;\">library<\/span> (factoextra)\n<span style=\"color: #993300;\">library<\/span> (cluster)<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u091a\u0930\u0923 2: \u0921\u0947\u091f\u093e \u0932\u094b\u0921 \u0915\u0930\u0947\u0902 \u0914\u0930 \u0924\u0948\u092f\u093e\u0930 \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0907\u0938 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0906\u0930 \u092e\u0947\u0902 \u0928\u093f\u0930\u094d\u092e\u093f\u0924 <em>\u092f\u0942\u090f\u0938\u090f\u0930\u0947\u0938\u094d\u091f\u094d\u0938<\/em> \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u093f\u0938\u092e\u0947\u0902 1973 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u092e\u0947\u0930\u093f\u0915\u0940 \u0930\u093e\u091c\u094d\u092f \u092e\u0947\u0902 <em>\u0939\u0924\u094d\u092f\u093e<\/em> , <em>\u0939\u092e\u0932\u0947<\/em> \u0914\u0930 <em>\u092c\u0932\u093e\u0924\u094d\u0915\u093e\u0930<\/em> \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0924\u093f 100,000 \u0932\u094b\u0917\u094b\u0902 \u092a\u0930 \u0917\u093f\u0930\u092b\u094d\u0924\u093e\u0930\u093f\u092f\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e, \u0938\u093e\u0925 \u0939\u0940 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0930\u093e\u091c\u094d\u092f \u0915\u0940 \u0936\u0939\u0930\u0940 \u0906\u092c\u093e\u0926\u0940 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0936\u0924 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0964 \u0915\u094d\u0937\u0947\u0924\u094d\u0930. , <em>\u0905\u0930\u094d\u092c\u0928\u092a\u0949\u092a<\/em> \u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u094b\u0921 \u0926\u093f\u0916\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><em>\u092f\u0942\u090f\u0938\u090f\u0905\u0930\u0947\u0938\u094d\u091f<\/em> \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u0932\u094b\u0921 \u0915\u0930\u0947\u0902<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0932\u0941\u092a\u094d\u0924 \u092e\u093e\u0928\u094b\u0902 \u0935\u093e\u0932\u0940 \u0938\u092d\u0940 \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u093e\u0901 \u0939\u091f\u093e\u090f\u0901<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091a\u0930 \u0915\u094b 0 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f \u0914\u0930 1 \u0915\u0947 \u092e\u093e\u0928\u0915 \u0935\u093f\u091a\u0932\u0928 \u0915\u0947 \u0938\u093e\u0925 \u0938\u094d\u0915\u0947\u0932 \u0915\u0930\u0947\u0902<\/span><\/li>\n<\/ul>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load data<\/span>\ndf &lt;-USArrests\n\n<span style=\"color: #008080;\">#remove rows with missing values<\/span><\/strong>\n<strong>df &lt;- na. <span style=\"color: #3366ff;\">omitted<\/span> (df)\n\n<span style=\"color: #008080;\">#scale each variable to have a mean of 0 and sd of 1<\/span><\/strong>\n<strong>df &lt;- scale(df)\n\n<span style=\"color: #008080;\">#view first six rows of dataset<\/span>\nhead(df)\n\n               Murder Assault UrbanPop Rape\nAlabama 1.24256408 0.7828393 -0.5209066 -0.003416473\nAlaska 0.50786248 1.1068225 -1.2117642 2.484202941\nArizona 0.07163341 1.4788032 0.9989801 1.042878388\nArkansas 0.23234938 0.2308680 -1.0735927 -0.184916602\nCalifornia 0.27826823 1.2628144 1.7589234 2.067820292\nColorado 0.02571456 0.3988593 0.8608085 1.864967207\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u091a\u0930\u0923 3: \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0907\u0937\u094d\u091f\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0906\u0930 \u092e\u0947\u0902 \u0915\u0947-\u092e\u0947\u0921\u0949\u0907\u0921 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e <strong>pam()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 &#8220;\u092e\u0927\u094d\u092f\u0938\u094d\u0925\u094b\u0902 \u0915\u0947 \u0906\u0938\u092a\u093e\u0938 \u0935\u093f\u092d\u093e\u091c\u0928&#8221; \u0914\u0930 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u093f\u0902\u091f\u0948\u0915\u094d\u0938 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u093e \u0939\u0948:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>pam(\u0921\u0947\u091f\u093e, k, \u092e\u0940\u091f\u094d\u0930\u093f\u0915 = &#8220;\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u093f\u092f\u0928&#8221;, \u0938\u094d\u091f\u0948\u0902\u0921 = \u0917\u0932\u0924)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0938\u094b\u0928\u093e:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u0921\u0947\u091f\u093e:<\/strong> \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u0915\u093e \u0928\u093e\u092e.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong> \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0964<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u092e\u0940\u091f\u094d\u0930\u093f\u0915:<\/strong> \u0926\u0942\u0930\u0940 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u092e\u0940\u091f\u094d\u0930\u093f\u0915\u0964 \u0921\u093f\u092b\u093c\u0949\u0932\u094d\u091f <em>\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u093f\u092f\u0928<\/em> \u0939\u0948 \u0932\u0947\u0915\u093f\u0928 \u0906\u092a <em>\u092e\u0948\u0928\u0939\u091f\u094d\u091f\u0928<\/em> \u092d\u0940 \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0938\u094d\u091f\u0948\u0902\u0921:<\/strong> \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u094b \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0915\u0930\u0928\u093e \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902\u0964 \u092e\u0942\u0932 \u092e\u0942\u0932\u094d\u092f \u0917\u0932\u0924 \u0939\u0948\u0964<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u091a\u0942\u0901\u0915\u093f \u0939\u092e \u092a\u0939\u0932\u0947 \u0938\u0947 \u0928\u0939\u0940\u0902 \u091c\u093e\u0928\u0924\u0947 \u0915\u093f \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0915\u094c\u0928 \u0938\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0907\u0937\u094d\u091f\u0924\u092e \u0939\u0948, \u0939\u092e \u0926\u094b \u0905\u0932\u0917-\u0905\u0932\u0917 \u0917\u094d\u0930\u093e\u092b\u093c \u092c\u0928\u093e\u090f\u0902\u0917\u0947 \u091c\u094b \u0939\u092e\u0947\u0902 \u0928\u093f\u0930\u094d\u0923\u092f \u0932\u0947\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947, \u0939\u092e \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u0940 \u0915\u0941\u0932 \u0938\u0902\u0916\u094d\u092f\u093e \u092c\u0928\u093e\u092e \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u090f\u0915 \u092a\u094d\u0932\u0949\u091f \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f <strong>fviz_nbclust()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>fviz_nbclust(df, pam, method = \u201c <span style=\"color: #008000;\">wss<\/span> \u201d)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12327 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kmedoide1.png\" alt=\"\u0915\u0947-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0915\u0947 \u0932\u093f\u090f \u0907\u0937\u094d\u091f\u0924\u092e \u0915\u094d\u0932\u0938\u094d\u091f\u0930\" width=\"462\" height=\"449\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 \u0939\u092e \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092c\u0922\u093c\u093e\u0924\u0947 \u0939\u0948\u0902, \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u0906\u092e \u0924\u094c\u0930 \u092a\u0930 \u0939\u092e\u0947\u0936\u093e \u092c\u0922\u093c\u0924\u093e \u091c\u093e\u090f\u0917\u093e\u0964 \u0907\u0938\u0932\u093f\u090f \u091c\u092c \u0939\u092e \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u093e \u092a\u094d\u0932\u0949\u091f \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u090f\u0915 &#8220;\u0918\u0941\u091f\u0928\u0947&#8221; \u0915\u0940 \u0924\u0932\u093e\u0936 \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u091c\u0939\u093e\u0902 \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 &#8220;\u091d\u0941\u0915\u0928\u093e&#8221; \u092f\u093e \u0938\u092e\u0924\u0932 \u0939\u094b\u0928\u093e \u0936\u0941\u0930\u0942 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0915\u0925\u093e\u0928\u0915 \u0915\u093e \u0935\u0915\u094d\u0930\u0924\u093e \u092c\u093f\u0902\u0926\u0941 \u0906\u092e \u0924\u094c\u0930 \u092a\u0930 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0907\u0937\u094d\u091f\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0906\u0902\u0915\u0921\u093c\u0947 \u0938\u0947 \u092a\u0930\u0947, <a href=\"https:\/\/statorials.org\/hi\/\u092e\u0936\u0940\u0928-\u0932\u0930\u094d\u0928\u093f\u0902\u0917-\u0913\u0935\u0930\u092b\u093f\u091f\u093f\u0902\u0917\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0913\u0935\u0930\u092b\u093f\u091f\u093f\u0902\u0917<\/a> \u0939\u094b\u0928\u0947 \u0915\u0940 \u0938\u0902\u092d\u093e\u0935\u0928\u093e \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0907\u0938 \u0917\u094d\u0930\u093e\u092b\u093c \u0915\u0947 \u0932\u093f\u090f, \u0910\u0938\u093e \u092a\u094d\u0930\u0924\u0940\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f k = 4 \u0938\u092e\u0942\u0939\u094b\u0902 \u092a\u0930 \u090f\u0915 \u091b\u094b\u091f\u093e \u0938\u093e \u092e\u094b\u0921\u093c \u092f\u093e &#8220;\u092e\u094b\u0921\u093c&#8221; \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092c\u0928\u093e\u092e \u0905\u0902\u0924\u0930\u093e\u0932 \u0906\u0901\u0915\u0921\u093c\u0947<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0907\u0937\u094d\u091f\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u090f\u0915 \u0905\u0928\u094d\u092f \u0924\u0930\u0940\u0915\u093e <a style=\"color: #000000;\" href=\"https:\/\/web.stanford.edu\/~hastie\/Papers\/gap.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">\u0935\u093f\u091a\u0932\u0928 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940<\/a> \u0928\u093e\u092e\u0915 \u090f\u0915 \u092e\u0940\u091f\u094d\u0930\u093f\u0915 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u0939\u0948, \u091c\u094b \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u0947 \u092c\u093f\u0928\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f \u0909\u0928\u0915\u0947 \u0905\u092a\u0947\u0915\u094d\u0937\u093f\u0924 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 k \u0915\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0915\u0941\u0932 \u0907\u0902\u091f\u094d\u0930\u093e-\u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u092d\u093f\u0928\u094d\u0928\u0924\u093e \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e <em>\u0915\u094d\u0932\u0938\u094d\u091f\u0930<\/em> \u092a\u0948\u0915\u0947\u091c \u0938\u0947 <strong>clusGap()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0915\u0940 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \u0905\u0902\u0924\u0930\u093e\u0932 \u0906\u0902\u0915\u0921\u093c\u094b\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0938\u093e\u0925 \u0939\u0940 <strong>fviz_gap_stat()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u092c\u0928\u093e\u092e \u0905\u0902\u0924\u0930\u093e\u0932 \u0906\u0902\u0915\u0921\u093c\u094b\u0902 \u0915\u0940 \u090f\u0915 \u0938\u093e\u091c\u093f\u0936 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate gap statistic based on number of clusters\n<\/span>gap_stat &lt;- clusGap(df,\n                    FUN = pam,\n                    K.max = 10, <span style=\"color: #008080;\">#max clusters to consider<\/span>\n                    B = 50) <span style=\"color: #008080;\">#total bootstrapped iterations<\/span>\n\n<span style=\"color: #008080;\">#plot number of clusters vs. gap statistic\n<\/span>fviz_gap_stat(gap_stat)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12328 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kmedoide2.png\" alt=\"\u0915\u0947-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0906\u0930 \u092e\u0947\u0902 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0907\u0937\u094d\u091f\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e\" width=\"443\" height=\"441\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0917\u094d\u0930\u093e\u092b\u093c \u0938\u0947, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0905\u0902\u0924\u0930\u093e\u0932 \u0906\u0901\u0915\u0921\u093c\u093e k = 4 \u0938\u092e\u0942\u0939\u094b\u0902 \u092a\u0930 \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948, \u091c\u094b \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0939\u0932\u0947 \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u0940 \u0917\u0908 \u0915\u094b\u0939\u0928\u0940 \u0935\u093f\u0927\u093f \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u091a\u0930\u0923 4: \u0911\u092a\u094d\u091f\u093f\u092e\u0932 <em>K<\/em> \u0915\u0947 \u0938\u093e\u0925 K-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0905\u0902\u0924 \u092e\u0947\u0902, \u0939\u092e 4 \u092e\u0947\u0902 \u0938\u0947 <em>k<\/em> \u0915\u0947 \u0932\u093f\u090f \u0907\u0937\u094d\u091f\u0924\u092e \u092e\u093e\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092a\u0930 k-medoids \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<span style=\"color: #000000;\">set.seed(1)<\/span>\n\n#perform k-medoids clustering with k = 4 clusters\n<\/span>kmed &lt;- pam(df, k = 4)\n\n<span style=\"color: #008080;\">#view results\n<\/span>kmed\n\n              ID Murder Assault UrbanPop Rape\nAlabama 1 1.2425641 0.7828393 -0.5209066 -0.003416473\nMichigan 22 0.9900104 1.0108275 0.5844655 1.480613993\nOklahoma 36 -0.2727580 -0.2371077 0.1699510 -0.131534211\nNew Hampshire 29 -1.3059321 -1.3650491 -0.6590781 -1.252564419\nVector clustering:\n       Alabama Alaska Arizona Arkansas California \n             1 2 2 1 2 \n      Colorado Connecticut Delaware Florida Georgia \n             2 3 3 2 1 \n        Hawaii Idaho Illinois Indiana Iowa \n             3 4 2 3 4 \n        Kansas Kentucky Louisiana Maine Maryland \n             3 3 1 4 2 \n Massachusetts Michigan Minnesota Mississippi Missouri \n             3 2 4 1 3 \n       Montana Nebraska Nevada New Hampshire New Jersey \n             3 3 2 4 3 \n    New Mexico New York North Carolina North Dakota Ohio \n             2 2 1 4 3 \n      Oklahoma Oregon Pennsylvania Rhode Island South Carolina \n             3 3 3 3 1 \n  South Dakota Tennessee Texas Utah Vermont \n             4 1 2 3 4 \n      Virginia Washington West Virginia Wisconsin Wyoming \n             3 3 4 4 3 \nObjective function:\n   build swap \n1.035116 1.027102 \n\nAvailable components:\n [1] \"medoids\" \"id.med\" \"clustering\" \"objective\" \"isolation\" \n [6] \"clusinfo\" \"silinfo\" \"diss\" \"call\" \"data\"          \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u0938\u092d\u0940 \u091a\u093e\u0930 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0938\u0947\u0902\u091f\u094d\u0930\u094b\u0907\u0921 \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092e\u0947\u0902 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0905\u0935\u0932\u094b\u0915\u0928 \u0939\u0948\u0902\u0964 \u0906\u0909\u091f\u092a\u0941\u091f \u0915\u0947 \u0936\u0940\u0930\u094d\u0937 \u0915\u0947 \u092a\u093e\u0938, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u091a\u093e\u0930 \u0915\u0947\u0928\u094d\u0926\u094d\u0930\u0915 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0905\u0935\u0938\u094d\u0925\u093e\u090f\u0901 \u0939\u0948\u0902:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0905\u0932\u093e\u092c\u093e\u092e\u093e<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u092e\u093f\u0936\u093f\u0917\u0928<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0913\u0915\u0932\u093e\u0939\u094b\u092e\u093e<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0928\u094d\u092f\u0942 \u0939\u0948\u092e\u094d\u092a\u0936\u093e\u092f\u0930<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u090f\u0915 \u0938\u094d\u0915\u0948\u091f\u0930\u092a\u094d\u0932\u0949\u091f \u092a\u0930 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0915\u0940 \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b <strong>fivz_cluster()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0905\u0915\u094d\u0937\u094b\u0902 \u092a\u0930 \u092a\u0939\u0932\u0947 \u0926\u094b \u092a\u094d\u0930\u092e\u0941\u0916 \u0918\u091f\u0915\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#plot results of final k-medoids model\n<span style=\"color: #000000;\">fviz_cluster(kmed, data = df)\n<\/span><\/span><\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12329 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kmedoide3.png\" alt=\"\u0906\u0930 \u092e\u0947\u0902 \u0915\u0947-\u092e\u0947\u0921\u0949\u0907\u0921 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u092a\u094d\u0932\u0949\u091f \u0915\u0930\u0928\u093e\" width=\"497\" height=\"500\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0930\u093e\u091c\u094d\u092f \u0915\u0947 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0905\u0938\u093e\u0907\u0928\u092e\u0947\u0902\u091f \u0915\u094b \u092e\u0942\u0932 \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092e\u0947\u0902 \u092d\u0940 \u091c\u094b\u0921\u093c \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#add cluster assignment to original data\n<span style=\"color: #000000;\">final_data &lt;- cbind(USArrests, cluster = kmed$cluster)\n<\/span>\n#view final data\n<span style=\"color: #000000;\">head(final_data)\n\n           Murder Assault UrbanPop Rape cluster\nAlabama 13.2 236 58 21.2 1\nAlaska 10.0 263 48 44.5 2\nArizona 8.1 294 80 31.0 2\nArkansas 8.8 190 50 19.5 1\nCalifornia 9.0 276 91 40.6 2\nColorado 7.9 204 78 38.7 2\n<\/span><\/span><\/strong><\/pre>\n<hr>\n<p> <span style=\"color: #000000;\">\u0906\u092a \u0907\u0938 \u0909\u0926\u093e\u0939\u0930\u0923 \u092e\u0947\u0902 \u092a\u094d\u0930\u092f\u0941\u0915\u094d\u0924 \u092a\u0942\u0930\u093e \u0906\u0930 \u0915\u094b\u0921 <a href=\"https:\/\/github.com\/Statorials\/R-Guides\/blob\/main\/k_medoids.R\" target=\"_blank\" rel=\"noopener noreferrer\">\u092f\u0939\u093e\u0902<\/a> \u092a\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u090f\u0915 \u092e\u0936\u0940\u0928 \u0932\u0930\u094d\u0928\u093f\u0902\u0917 \u0924\u0915\u0928\u0940\u0915 \u0939\u0948 \u091c\u094b \u0921\u0947\u091f\u093e \u0938\u0947\u091f \u0915\u0947 \u092d\u0940\u0924\u0930 \u0938\u092e\u0942\u0939\u094b\u0902 \u092f\u093e \u0905\u0935\u0932\u094b\u0915\u0928\u094b\u0902 \u0915\u0947 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u094b \u0916\u094b\u091c\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u0932\u0915\u094d\u0937\u094d\u092f \u0910\u0938\u0947 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u094b \u0922\u0942\u0902\u0922\u0928\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u094d\u0932\u0938\u094d\u091f\u0930 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0905\u0935\u0932\u094b\u0915\u0928 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0902, \u091c\u092c\u0915\u093f \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u092e\u0942\u0939\u094b\u0902 \u092e\u0947\u0902 \u0905\u0935\u0932\u094b\u0915\u0928 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0938\u0947 \u0915\u093e\u092b\u0940 \u092d\u093f\u0928\u094d\u0928 \u0939\u094b\u0902\u0964 \u0915\u094d\u0932\u0938\u094d\u091f\u0930\u093f\u0902\u0917 \u092c\u093f\u0928\u093e \u092a\u0930\u094d\u092f\u0935\u0947\u0915\u094d\u0937\u093f\u0924 \u0936\u093f\u0915\u094d\u0937\u0923 \u0915\u093e \u090f\u0915 \u0930\u0942\u092a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1245","post","type-post","status-publish","format-standard","hentry","category-3"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0906\u0930 \u092e\u0947\u0902 \u0915\u0947-\u092e\u0947\u0921\u094b\u0907\u0921\u094d\u0938: \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u0909\u0926\u093e\u0939\u0930\u0923<\/title>\n<meta name=\"description\" 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\u092c\u0947\u0902\u091c\u093e\u092e\u093f\u0928 \u090f\u0902\u0921\u0930\u0938\u0928\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0926\u094d\u0935\u093e\u0930\u093e \u0932\u093f\u0916\u093f\u0924\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u0921\u0949. \u092c\u0947\u0902\u091c\u093e\u092e\u093f\u0928 \u090f\u0902\u0921\u0930\u0938\u0928\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u0905\u0928\u0941\u092e\u093e\u0928\u093f\u0924 \u092a\u0922\u093c\u0928\u0947 \u0915\u093e \u0938\u092e\u092f\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 \u092e\u093f\u0928\u091f\" \/>\n<script type=\"application\/ld+json\" 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