{"id":1643,"date":"2023-07-25T13:22:41","date_gmt":"2023-07-25T13:22:41","guid":{"rendered":"https:\/\/statorials.org\/tr\/rand-indeksi\/"},"modified":"2023-07-25T13:22:41","modified_gmt":"2023-07-25T13:22:41","slug":"rand-indeksi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rand-indeksi\/","title":{"rendered":"Rand endeksi nedir? (tan\u0131m ve \u00f6rnekler)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Rand endeksi,<\/strong> iki farkl\u0131 k\u00fcmeleme y\u00f6ntemi aras\u0131ndaki sonu\u00e7lar\u0131n benzerli\u011fini kar\u015f\u0131la\u015ft\u0131rman\u0131n bir yoludur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c7o\u011funlukla <em>R<\/em> olarak g\u00f6sterilen Rand endeksi \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>R<\/em> = (a+b) \/ ( <sub>nC2<\/sub> <sub>)<\/sub><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>a:<\/strong> iki k\u00fcmeleme y\u00f6ntemine g\u00f6re bir \u00f6\u011fe \u00e7iftinin ayn\u0131 k\u00fcmeye ait olma say\u0131s\u0131.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b:<\/strong> iki k\u00fcmeleme y\u00f6ntemine g\u00f6re bir \u00f6\u011fe \u00e7iftinin fark k\u00fcmelerine ait olma say\u0131s\u0131.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n<\/sub> C <sub>2<\/sub> :<\/strong> <em>n<\/em> elemanl\u0131 bir k\u00fcmedeki s\u0131ras\u0131z \u00e7iftlerin say\u0131s\u0131.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Rand endeksi her zaman 0 ile 1 aras\u0131nda bir de\u011fer al\u0131r; burada:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>0:<\/strong> \u0130ki k\u00fcmeleme y\u00f6nteminin bir \u00e7ift \u00f6\u011fenin k\u00fcmelenmesi konusunda anla\u015fmaya varmad\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>1:<\/strong> \u0130ki k\u00fcmeleme y\u00f6nteminin, her bir \u00f6\u011fe \u00e7iftinin k\u00fcmelenmesi konusunda m\u00fckemmel \u015fekilde uyu\u015ftu\u011funu belirtir.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek, basit bir veri k\u00fcmesi i\u00e7in iki k\u00fcmeleme y\u00f6ntemi aras\u0131nda Rand dizininin nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Rand endeksi nas\u0131l hesaplan\u0131r?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Be\u015f \u00f6\u011feden olu\u015fan a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Veri k\u00fcmesi: {A, B, C, D, E}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ve her bir \u00f6\u011feyi a\u015fa\u011f\u0131daki k\u00fcmelere yerle\u015ftiren iki k\u00fcmeleme y\u00f6ntemi kulland\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Y\u00f6ntem 1 k\u00fcmeleri: {1, 1, 1, 2, 2}<\/span><\/li>\n<li> <span style=\"color: #000000;\">K\u00fcme y\u00f6ntemi 2: {1, 1, 2, 2, 3}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu k\u00fcmeleme y\u00f6ntemleri aras\u0131nda Rand endeksini hesaplamak i\u00e7in \u00f6ncelikle be\u015f \u00f6\u011feli veri k\u00fcmesindeki t\u00fcm olas\u0131 s\u0131ras\u0131z \u00e7iftleri yazmam\u0131z gerekir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">S\u0131ras\u0131z \u00e7iftler: {A, B}, {A, C}, {A, D}, {A, E}, {B, C}, {B, D}, {B, E}, {C, D } , {C, E}, {D, E}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>10 tane<\/strong> s\u0131ras\u0131z \u00e7ift vard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, her iki k\u00fcmeleme y\u00f6nteminde de ayn\u0131 k\u00fcmeye ait s\u0131ras\u0131z \u00e7iftlerin say\u0131s\u0131n\u0131 temsil eden <strong>a&#8217;y\u0131<\/strong> hesaplamam\u0131z gerekir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">{AB}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu durumda a = <strong>1<\/strong> olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, iki k\u00fcmeleme y\u00f6nteminde farkl\u0131 k\u00fcmelere ait s\u0131ras\u0131z \u00e7iftlerin say\u0131s\u0131n\u0131 temsil eden <strong>b&#8217;yi<\/strong> hesaplamam\u0131z gerekir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">{A, D}, {A, E}, {B, D}, {B, E}, {C, E}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu durumda b = <strong>5<\/strong> olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak Rand indeksini \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><em>R<\/em> = (a+b) \/ ( <sub>nC2<\/sub> <sub>)<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\"><em>R<\/em> = (1+5) \/ 10<\/span><\/li>\n<li> <span style=\"color: #000000;\"><em>R<\/em> = 6\/10<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Rand endeksi <strong>0,6&#8217;d\u0131r<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>R&#8217;de Rand endeksi nas\u0131l hesaplan\u0131r<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">R&#8217;deki iki k\u00fcmeleme y\u00f6ntemi aras\u0131ndaki Rand indeksini hesaplamak i\u00e7in <strong>fosil<\/strong> paketindeki <strong>Rand.index()<\/strong> fonksiyonunu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #993300;\">library<\/span> (fossil)\n\n<span style=\"color: #008080;\">#define clusters\n<\/span>method1 &lt;- c(1, 1, 1, 2, 2)\nmethod2 &lt;- c(1, 1, 2, 2, 3)\n\n<span style=\"color: #008080;\">#calculate Rand index between clustering methods\n<\/span>rand. <span style=\"color: #3366ff;\">index<\/span> (method1, method2)\n\n[1] 0.6\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Rand endeksi <strong>0,6&#8217;d\u0131r<\/strong> . Bu bizim manuel olarak hesaplad\u0131\u011f\u0131m\u0131z de\u011fere kar\u015f\u0131l\u0131k geliyor.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Python&#8217;da Rand Dizini Nas\u0131l Hesaplan\u0131r?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130ki k\u00fcme aras\u0131ndaki Rand indeksini hesaplamak i\u00e7in Python&#8217;da a\u015fa\u011f\u0131daki fonksiyonu tan\u0131mlayabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">special<\/span> <span style=\"color: #008000;\">import<\/span> comb\n\n<span style=\"color: #008080;\">#define Rand index function\n<\/span><span style=\"color: #008000;\">def<\/span> <span style=\"color: #993300;\">rand_index<\/span> (actual, pred):\n\n    tp_plus_fp = comb(np. <span style=\"color: #3366ff;\">bincount<\/span> (actual), 2). <span style=\"color: #3366ff;\">sum<\/span> ()\n    tp_plus_fn = comb(np. <span style=\"color: #3366ff;\">bincount<\/span> (pred), 2). <span style=\"color: #3366ff;\">sum<\/span> ()\n    A = np. <span style=\"color: #3366ff;\">c_<\/span> [(actual, pred)]\n    tp = sum(comb( <span style=\"color: #3366ff;\">np.bincount<\/span> (A[A[:, 0] == i, 1]), 2) <span style=\"color: #3366ff;\">.sum<\/span> ()\n             <span style=\"color: #008000;\">for<\/span> i <span style=\"color: #008000;\">in<\/span> set(actual))\n    fp = tp_plus_fp - tp\n    fn = tp_plus_fn - tp\n    tn = comb(len(A), 2) - tp - fp - fn\n    <span style=\"color: #008000;\">return<\/span> (tp + tn) \/ (tp + fp + fn + tn)\n\n<span style=\"color: #008080;\">#calculate Rand index\n<\/span>rand_index([1, 1, 1, 2, 2], [1, 1, 2, 2, 3])\n\n0.6<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Rand endeksi <strong>0,6<\/strong> olarak \u00e7\u0131k\u0131yor. Bu, \u00f6nceki \u00f6rneklerde hesaplanan de\u011fere kar\u015f\u0131l\u0131k gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/k-rde-gruplama-anlamina-gelir\/\" target=\"_blank\" rel=\"noopener\">K-Means K\u00fcmelenmesine Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/rdeki-k-medoidler\/\" target=\"_blank\" rel=\"noopener\">K-Medoids k\u00fcmelemeye giri\u015f<\/a><br \/> Hiyerar\u015fik k\u00fcmelemeye giri\u015f<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rand endeksi, iki farkl\u0131 k\u00fcmeleme y\u00f6ntemi aras\u0131ndaki sonu\u00e7lar\u0131n benzerli\u011fini kar\u015f\u0131la\u015ft\u0131rman\u0131n bir yoludur. \u00c7o\u011funlukla R olarak g\u00f6sterilen Rand endeksi \u015fu \u015fekilde hesaplan\u0131r: R = (a+b) \/ ( nC2 ) Alt\u0131n: a: iki k\u00fcmeleme y\u00f6ntemine g\u00f6re bir \u00f6\u011fe \u00e7iftinin ayn\u0131 k\u00fcmeye ait olma say\u0131s\u0131. b: iki k\u00fcmeleme y\u00f6ntemine g\u00f6re bir \u00f6\u011fe \u00e7iftinin fark k\u00fcmelerine ait olma say\u0131s\u0131. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1643","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Rand Endeksi nedir? 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