{"id":14304,"date":"2024-01-04T18:57:22","date_gmt":"2024-01-04T15:27:22","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/k-means-clustering-%d8%a8%d8%a7-%d8%b1%d9%88%d8%b4-elbow\/"},"modified":"2024-01-04T18:57:22","modified_gmt":"2024-01-04T15:27:22","slug":"k-means-clustering-%d8%a8%d8%a7-%d8%b1%d9%88%d8%b4-elbow","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/k-means-clustering-%d8%a8%d8%a7-%d8%b1%d9%88%d8%b4-elbow\/","title":{"rendered":"K-Means Clustering \u0628\u0627 \u0631\u0648\u0634 Elbow"},"content":{"rendered":"<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\"> 3<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<p>\u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc K-means \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0628\u062f\u0648\u0646 \u0646\u0638\u0627\u0631\u062a \u0627\u0633\u062a \u06a9\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u06af\u0631\u0648\u0647 \u0628\u0646\u062f\u06cc \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u0647\u0631 \u0646\u0642\u0637\u0647 \u0641\u0627\u0635\u0644\u0647 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u062a\u0627 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0645\u0631\u06a9\u0632\u06cc \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f <em>\u0646\u0642\u0637\u0647 \u0645\u0631\u06a9\u0632\u06cc<\/em>.  \u0645\u0631\u06a9\u0632\u0647\u0627 \u0628\u0647 \u0648\u0633\u06cc\u0644\u0647 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637\u06cc \u06a9\u0647 \u062f\u0631 \u06cc\u06a9 \u062e\u0648\u0634\u0647 \u0647\u0633\u062a\u0646\u062f \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u0646\u062f.  \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0628\u062a\u062f\u0627 \u0646\u0642\u0627\u0637 \u062a\u0635\u0627\u062f\u0641\u06cc \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u0631\u06a9\u0632 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0633\u067e\u0633 \u062a\u0646\u0638\u06cc\u0645 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062a\u0627 \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u06a9\u0627\u0645\u0644 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<blockquote>\n<p>\u0646\u06a9\u062a\u0647 \u0645\u0647\u0645\u06cc \u06a9\u0647 \u0647\u0646\u06af\u0627\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 K-means \u0628\u0627\u06cc\u062f \u0628\u0647 \u062e\u0627\u0637\u0631 \u0628\u0633\u067e\u0627\u0631\u06cc\u062f \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627 \u06cc\u06a9 \u0641\u0631\u0627\u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0627\u0633\u062a \u06a9\u0647 \u0642\u0628\u0644 \u0627\u0632 \u0627\u062c\u0631\u0627\u06cc \u0645\u062f\u0644 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<\/blockquote>\n<p>K-means \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Scikit-Learn \u062a\u0646\u0647\u0627 \u0628\u0627 3 \u062e\u0637 \u06a9\u062f \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0631\u062f.  Scikit-Learn \u0647\u0645\u0686\u0646\u06cc\u0646 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u06cc\u06a9 \u0631\u0648\u0634 \u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc centroid \u062f\u0631 \u062f\u0633\u062a\u0631\u0633 \u062f\u0627\u0631\u062f\u060c <em>kmeans++<\/em>\u060c \u06a9\u0647 \u0628\u0647 \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u0633\u0631\u06cc\u0639\u062a\u0631 \u0645\u062f\u0644 \u06a9\u0645\u06a9 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0627\u0639\u0645\u0627\u0644 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc K-means\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc \u0634\u0648\u062f <em>\u067e\u0646\u06af\u0648\u0626\u0646 \u0647\u0627\u06cc \u067e\u0627\u0644\u0645\u0631<\/em> \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u060c \u0633\u062a\u0648\u0646\u200c\u0647\u0627\u06cc\u06cc \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u0648 \u0627\u0632 Seaborn \u0628\u0631\u0627\u06cc \u0631\u0633\u0645 \u0646\u0645\u0648\u062f\u0627\u0631 \u067e\u0631\u0627\u06a9\u0646\u062f\u06af\u06cc \u0628\u0627 \u062e\u0648\u0634\u0647\u200c\u0647\u0627\u06cc \u06a9\u062f \u0631\u0646\u06af\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \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>: \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u0627\u0632 \u0627\u06cc\u0646\u062c\u0627 \u062f\u0627\u0646\u0644\u0648\u062f \u06a9\u0646\u06cc\u062f <a href=\"https:\/\/gist.github.com\/cassiasamp\/197b4e070f5f4da890ca4d226d088d1f\" target=\"_blank\" rel=\"noopener\">\u0627\u0631\u062a\u0628\u0627\u0637 \u062f\u0627\u062f\u0646<\/a>.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f import \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0647\u0627 \u0648 \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u067e\u0646\u06af\u0648\u0626\u0646 \u0647\u0627\u060c \u0628\u0631\u0634 \u0622\u0646 \u0628\u0647 \u0633\u062a\u0648\u0646 \u0647\u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0634\u062f\u0647 \u0648 \u0631\u0647\u0627 \u06a9\u0631\u062f\u0646 \u0631\u062f\u06cc\u0641 \u0647\u0627\u06cc\u06cc \u0628\u0627 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0627\u0632 \u062f\u0633\u062a \u0631\u0641\u062a\u0647 (\u0641\u0642\u0637 2 \u0645\u0648\u0631\u062f \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f):<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> pandas <span class=\"hljs-keyword\">as<\/span> pd\n<span class=\"hljs-keyword\">import<\/span> seaborn <span class=\"hljs-keyword\">as<\/span> sns\n<span class=\"hljs-keyword\">import<\/span> matplotlib.pyplot <span class=\"hljs-keyword\">as<\/span> plt\n<span class=\"hljs-keyword\">from<\/span> sklearn.cluster <span class=\"hljs-keyword\">import<\/span> KMeans\n\ndf = pd.read_csv(<span class=\"hljs-string\">'penguins.csv'<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(df.shape) \ndf = df((<span class=\"hljs-string\">'bill_length_mm'<\/span>, <span class=\"hljs-string\">'flipper_length_mm'<\/span>))\ndf = df.dropna(axis=<span class=\"hljs-number\">0<\/span>)\n<\/code><\/pre>\n<p>\u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0631\u0648\u0634 Elbow \u0628\u0631\u0627\u06cc \u062f\u0627\u0634\u062a\u0646 \u0646\u0634\u0627\u0646\u0647 \u0627\u06cc \u0627\u0632 \u062e\u0648\u0634\u0647 \u0647\u0627 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u062e\u0648\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645.  \u0627\u06cc\u0646 \u0634\u0627\u0645\u0644 \u062a\u0641\u0633\u06cc\u0631 \u06cc\u06a9 \u0637\u0631\u062d \u062e\u0637\u06cc \u0628\u0627 \u0634\u06a9\u0644 \u0622\u0631\u0646\u062c \u0627\u0633\u062a.  \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627 \u062c\u0627\u06cc\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0622\u0631\u0646\u062c \u062e\u0645 \u0645\u06cc \u0634\u0648\u062f.  \u0645\u062d\u0648\u0631 x \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627 \u0648 \u0645\u062d\u0648\u0631 y \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u062f\u0631\u0648\u0646 \u062e\u0648\u0634\u0647 \u0647\u0627 (WCSS) \u0628\u0631\u0627\u06cc \u0647\u0631 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">wcss = ()\n\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    clustering = KMeans(n_clusters=i, init=<span class=\"hljs-string\">'k-means++'<\/span>, random_state=<span class=\"hljs-number\">42<\/span>)\n    clustering.fit(df)\n    wcss.append(clustering.inertia_)\n    \nks = (<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>)\nsns.lineplot(x = ks, y = wcss);\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/k-means-clustering-with-the-elbow-method-1.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0631\u0648\u0634 elbow \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0627 \u062f\u0627\u0631\u0627\u06cc 2 \u062e\u0648\u0634\u0647 \u0627\u0633\u062a.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0642\u0628\u0644 \u0648 \u0628\u0639\u062f \u0627\u0632 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">fig, axes = plt.subplots(nrows=<span class=\"hljs-number\">1<\/span>, ncols=<span class=\"hljs-number\">2<\/span>, figsize=(<span class=\"hljs-number\">15<\/span>,<span class=\"hljs-number\">5<\/span>))\nsns.scatterplot(ax=axes(<span class=\"hljs-number\">0<\/span>), data=df, x=<span class=\"hljs-string\">'bill_length_mm'<\/span>, y=<span class=\"hljs-string\">'flipper_length_mm'<\/span>).set_title(<span class=\"hljs-string\">'Without clustering'<\/span>)\nsns.scatterplot(ax=axes(<span class=\"hljs-number\">1<\/span>), data=df, x=<span class=\"hljs-string\">'bill_length_mm'<\/span>, y=<span class=\"hljs-string\">'flipper_length_mm'<\/span>, hue=clustering.labels_).set_title(<span class=\"hljs-string\">'Using the elbow method'<\/span>);\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/k-means-clustering-with-the-elbow-method-2.png\" alt=\"\" title=\"\"><\/p>\n<blockquote>\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 \u0631\u0648\u0634 Elbow \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u062a\u0646\u0647\u0627 \u06cc\u06a9 \u0645\u0631\u062c\u0639 \u0627\u0633\u062a.  \u0645\u0627 \u0642\u0628\u0644\u0627\u064b \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0645\u0627 3 \u0646\u0648\u0639 \u067e\u0646\u06af\u0648\u0626\u0646 \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062f\u0627\u0631\u06cc\u0645\u060c \u0627\u0645\u0627 \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u062a\u0639\u062f\u0627\u062f \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 Elbow \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u06cc\u0645\u060c 2 \u062e\u0648\u0634\u0647 \u0646\u062a\u06cc\u062c\u0647 \u0645\u0627 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n<\/blockquote>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 K-means \u0628\u0647 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u062f\u0627\u062f\u0647 \u0647\u0627 \u062d\u0633\u0627\u0633 \u0627\u0633\u062a\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u0622\u0645\u0627\u0631 \u062a\u0648\u0635\u06cc\u0641\u06cc \u0633\u062a\u0648\u0646 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0631 \u062d\u0627\u0644 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0647\u0633\u062a\u06cc\u0645 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">df.describe().T \n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u062f\u0631:<\/p>\n<pre><code class=\"hljs\"> \t\t\t\t\tcount \tmean \t\tstd \t\tmin \t25% \t50% \t75% \tmax\nbill_length_mm \t\t342.0 \t43.921930 \t5.459584 \t32.1 \t39.225 \t44.45 \t48.5 \t59.6\nflipper_length_mm \t342.0 \t200.915205 \t14.061714 \t172.0 \t190.000 197.00 \t213.0 \t231.0\n<\/code><\/pre>\n<p>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0627\u0632 \u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f (std) \u062f\u0648\u0631 \u0627\u0633\u062a\u060c \u0627\u06cc\u0646 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u0628\u0627\u0644\u0627 \u0627\u0633\u062a.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0633\u0639\u06cc \u06a9\u0646\u06cc\u0645 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0645\u0642\u06cc\u0627\u0633 \u062f\u0627\u062f\u0646 \u0628\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0628\u0627 \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f Scaler \u06a9\u0627\u0647\u0634 \u062f\u0647\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">from<\/span> sklearn.preprocessing <span class=\"hljs-keyword\">import<\/span> StandardScaler\n\nss = StandardScaler()\nscaled = ss.fit_transform(df)\n<\/code><\/pre>\n<p>\u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0631\u0648\u0634 Elbow \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u06a9\u0646\u06cc\u0645 process \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0642\u06cc\u0627\u0633 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647:<\/p>\n<pre><code class=\"hljs\">wcss_sc = ()\n\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    clustering_sc = KMeans(n_clusters=i, init=<span class=\"hljs-string\">'k-means++'<\/span>, random_state=<span class=\"hljs-number\">42<\/span>)\n    clustering_sc.fit(scaled)\n    wcss_sc.append(clustering_sc.inertia_)\n    \nks = (<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>)\nsns.lineplot(x = ks, y = wcss_sc);\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/k-means-clustering-with-the-elbow-method-3.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0627\u06cc\u0646 \u0628\u0627\u0631\u060c \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647\u200c\u0647\u0627\u06cc \u067e\u06cc\u0634\u0646\u0647\u0627\u062f\u06cc 3 \u0627\u0633\u062a. \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0631\u0627 \u0628\u0627 \u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0628\u0647 \u0647\u0645\u0631\u0627\u0647 \u062f\u0648 \u0646\u0645\u0648\u062f\u0627\u0631 \u0642\u0628\u0644\u06cc \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647 \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">fig, axes = plt.subplots(nrows=<span class=\"hljs-number\">1<\/span>, ncols=<span class=\"hljs-number\">3<\/span>, figsize=(<span class=\"hljs-number\">15<\/span>,<span class=\"hljs-number\">5<\/span>))\nsns.scatterplot(ax=axes(<span class=\"hljs-number\">0<\/span>), data=df, x=<span class=\"hljs-string\">'bill_length_mm'<\/span>, y=<span class=\"hljs-string\">'flipper_length_mm'<\/span>).set_title(<span class=\"hljs-string\">'Without clustering'<\/span>)\nsns.scatterplot(ax=axes(<span class=\"hljs-number\">1<\/span>), data=df, x=<span class=\"hljs-string\">'bill_length_mm'<\/span>, y=<span class=\"hljs-string\">'flipper_length_mm'<\/span>, hue=clustering.labels_).set_title(<span class=\"hljs-string\">'With the Elbow method'<\/span>)\nsns.scatterplot(ax=axes(<span class=\"hljs-number\">2<\/span>), data=df, x=<span class=\"hljs-string\">'bill_length_mm'<\/span>, y=<span class=\"hljs-string\">'flipper_length_mm'<\/span>, hue=clustering_sc.labels_).set_title(<span class=\"hljs-string\">'With the Elbow method and scaled data'<\/span>);\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/k-means-clustering-with-the-elbow-method-4.png\" alt=\"\" title=\"\"><\/p>\n<p>\u0647\u0646\u06af\u0627\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 K-means Clustering\u060c \u0628\u0627\u06cc\u062f \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647 \u0647\u0627 \u0631\u0627 \u0627\u0632 \u0642\u0628\u0644 \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u06cc\u062f.  \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0647\u0646\u06af\u0627\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634\u06cc \u0628\u0631\u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u062e\u0648\u062f \u062f\u06cc\u062f\u06cc\u0645 <em>\u06a9<\/em> \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647\u200c\u0647\u0627\u060c \u0646\u062a\u06cc\u062c\u0647 \u0641\u0642\u0637 \u06cc\u06a9 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0627\u0633\u062a \u0648 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u062a\u062d\u062a \u062a\u0623\u062b\u06cc\u0631 \u0645\u06cc\u0632\u0627\u0646 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0628\u0627\u0634\u062f.  \u0627\u0646\u062c\u0627\u0645 \u06cc\u06a9 \u062a\u062d\u0644\u06cc\u0644 \u0639\u0645\u06cc\u0642 \u0648 \u062a\u0648\u0644\u06cc\u062f \u0628\u06cc\u0634 \u0627\u0632 \u06cc\u06a9 \u0645\u062f\u0644 \u0628\u0627 _k_\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0647\u0646\u06af\u0627\u0645 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0645\u0647\u0645 \u0627\u0633\u062a.<\/p>\n<p>\u0627\u06af\u0631 \u0647\u06cc\u0686 \u0646\u0634\u0627\u0646\u0647 \u0642\u0628\u0644\u06cc \u0627\u0632 \u062a\u0639\u062f\u0627\u062f \u062e\u0648\u0634\u0647\u200c\u0647\u0627 \u062f\u0631 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f\u060c \u0622\u0646 \u0631\u0627 \u062a\u062c\u0633\u0645 \u06a9\u0646\u06cc\u062f\u060c \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\u062f \u0648 \u062a\u0641\u0633\u06cc\u0631 \u06a9\u0646\u06cc\u062f \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u062f \u0622\u06cc\u0627 \u0646\u062a\u0627\u06cc\u062c \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0645\u0646\u0637\u0642\u06cc \u0627\u0633\u062a \u06cc\u0627 \u062e\u06cc\u0631.  \u0627\u06af\u0631 \u0646\u0647\u060c \u062f\u0648\u0628\u0627\u0631\u0647 \u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc \u06a9\u0646\u06cc\u062f.  \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0628\u0647 \u0628\u06cc\u0634 \u0627\u0632 \u06cc\u06a9 \u0645\u062a\u0631\u06cc\u06a9 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u062f \u0648 \u0645\u062f\u0644\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0631\u0627 \u0646\u0645\u0648\u0646\u0647\u200c\u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u062f &#8211; \u0628\u0631\u0627\u06cc K-means\u060c \u0628\u0647 \u0627\u0645\u062a\u06cc\u0627\u0632 silhouette \u0648 \u0634\u0627\u06cc\u062f \u062e\u0648\u0634\u0647\u200c\u0628\u0646\u062f\u06cc \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628\u06cc \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u062f \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u062f \u0622\u06cc\u0627 \u0646\u062a\u0627\u06cc\u062c \u06cc\u06a9\u0633\u0627\u0646 \u0645\u06cc\u200c\u0645\u0627\u0646\u0646\u062f \u06cc\u0627 \u062e\u06cc\u0631.<\/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 18:57:11<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;14304&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;K-Means Clustering \u0628\u0627 \u0631\u0648\u0634 Elbow&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\"> 3<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u062e\u0648\u0634\u0647 \u0628\u0646\u062f\u06cc K-means \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0628\u062f\u0648\u0646 \u0646\u0638\u0627\u0631\u062a \u0627\u0633\u062a \u06a9\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u06af\u0631\u0648\u0647 \u0628\u0646\u062f\u06cc \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u0647\u0631 \u0646\u0642\u0637\u0647 \u0641\u0627\u0635\u0644\u0647 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u062a\u0627 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0645\u0631\u06a9\u0632\u06cc \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u0646\u0642\u0637\u0647 \u0645\u0631\u06a9\u0632\u06cc. \u0645\u0631\u06a9\u0632\u0647\u0627 \u0628\u0647 \u0648\u0633\u06cc\u0644\u0647 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637\u06cc \u06a9\u0647 \u062f\u0631 \u06cc\u06a9 \u062e\u0648\u0634\u0647 \u0647\u0633\u062a\u0646\u062f \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u0646\u062f. \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0628\u062a\u062f\u0627 \u0646\u0642\u0627\u0637 \u062a\u0635\u0627\u062f\u0641\u06cc \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u0631\u06a9\u0632 \u0627\u0646\u062a\u062e\u0627\u0628 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":14305,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[],"class_list":["post-14304","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\/14304","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=14304"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/14304\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/14305"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=14304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=14304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=14304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}