{"id":1643,"date":"2023-07-25T13:22:41","date_gmt":"2023-07-25T13:22:41","guid":{"rendered":"https:\/\/statorials.org\/id\/indeks-rand\/"},"modified":"2023-07-25T13:22:41","modified_gmt":"2023-07-25T13:22:41","slug":"indeks-rand","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/indeks-rand\/","title":{"rendered":"Apa itu indeks rand? (definisi &amp; contoh)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Indeks Rand<\/strong> adalah cara untuk membandingkan kesamaan hasil antara dua metode pengelompokan yang berbeda.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Sering dilambangkan <em>R<\/em> , indeks Rand dihitung sebagai berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>R<\/em> = (a+b) \/ ( <sub>n<\/sub> C <sub>2<\/sub> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>a:<\/strong> berapa kali sepasang elemen menjadi anggota cluster yang sama menurut dua metode clustering.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b:<\/strong> berapa kali sepasang elemen termasuk dalam cluster yang berbeda menurut dua metode pengelompokan.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n<\/sub> C <sub>2<\/sub> :<\/strong> Banyaknya pasangan tak berurutan dalam himpunan yang terdiri dari <em>n<\/em> elemen.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Indeks Rand selalu mengambil nilai antara 0 dan 1 dimana:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>0:<\/strong> menunjukkan bahwa dua metode pengelompokan tidak menyetujui pengelompokan sepasang elemen.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>1:<\/strong> Menunjukkan bahwa dua metode pengelompokan sangat cocok dalam pengelompokan setiap pasangan elemen.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Contoh berikut mengilustrasikan cara menghitung indeks Rand antara dua metode pengelompokan untuk kumpulan data sederhana.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Contoh: Cara menghitung indeks Rand<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Misalkan kita memiliki kumpulan data berikut yang terdiri dari lima elemen:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Kumpulan data: {A, B, C, D, E}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Dan misalkan kita menggunakan dua metode pengelompokan yang menempatkan setiap elemen ke dalam kelompok berikut:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Cluster metode 1: {1, 1, 1, 2, 2}<\/span><\/li>\n<li> <span style=\"color: #000000;\">Metode cluster 2: {1, 1, 2, 2, 3}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Untuk menghitung indeks Rand antara metode pengelompokan ini, pertama-tama kita perlu menuliskan semua kemungkinan pasangan tak berurutan dalam kumpulan data lima elemen:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Pasangan tak berurutan: {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;\">Ada <strong>10<\/strong> pasangan tak berurutan.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Selanjutnya, kita perlu menghitung <strong>a<\/strong> , yang mewakili jumlah pasangan tak berurutan yang termasuk dalam cluster yang sama di kedua metode clustering:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">{AB}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Dalam hal ini, a = <strong>1<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Selanjutnya, kita perlu menghitung <strong>b<\/strong> , yang mewakili jumlah pasangan tak berurutan milik cluster berbeda dalam dua metode clustering:<\/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;\">Dalam hal ini, b = <strong>5<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Terakhir, kita dapat menghitung indeks Rand sebagai berikut:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><em>R<\/em> = (a+b) \/ ( <sub>n<\/sub> C <sub>2<\/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;\">Indeks Rand adalah <strong>0,6<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Cara menghitung indeks Rand di R<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Kita dapat menggunakan fungsi <strong>rand.index()<\/strong> dari paket <strong>fosil<\/strong> untuk menghitung indeks Rand antara dua metode pengelompokan di R:<\/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;\">Indeks Rand adalah <strong>0,6<\/strong> . Ini sesuai dengan nilai yang kami hitung secara manual.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Cara Menghitung Indeks Rand dengan Python<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Kita dapat mendefinisikan fungsi berikut dengan Python untuk menghitung indeks Rand antara dua cluster:<\/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;\">Indeks Rand ternyata <strong>0,6<\/strong> . Ini sesuai dengan nilai yang dihitung pada contoh sebelumnya.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Sumber daya tambahan<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/id\/k-berarti-mengelompokkan-dalam-r\/\" target=\"_blank\" rel=\"noopener\">Pengantar Pengelompokan K-Means<\/a><br \/> <a href=\"https:\/\/statorials.org\/id\/k-medoid-di-sungai\/\" target=\"_blank\" rel=\"noopener\">Pengantar pengelompokan K-Medoids<\/a><br \/> Pengantar pengelompokan hierarki<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Indeks Rand adalah cara untuk membandingkan kesamaan hasil antara dua metode pengelompokan yang berbeda. Sering dilambangkan R , indeks Rand dihitung sebagai berikut: R = (a+b) \/ ( n C 2 ) Emas: a: berapa kali sepasang elemen menjadi anggota cluster yang sama menurut dua metode clustering. b: berapa kali sepasang elemen termasuk dalam cluster [&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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Apa itu Indeks Rand? 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