{"id":1642,"date":"2023-07-25T13:22:41","date_gmt":"2023-07-25T13:22:41","guid":{"rendered":"https:\/\/statorials.org\/pt\/indice-de-rands\/"},"modified":"2023-07-25T13:22:41","modified_gmt":"2023-07-25T13:22:41","slug":"indice-de-rands","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/indice-de-rands\/","title":{"rendered":"O que \u00e9 o \u00edndice rand? (defini\u00e7\u00e3o e exemplos)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">O <strong>\u00edndice Rand<\/strong> \u00e9 uma forma de comparar a similaridade de resultados entre dois m\u00e9todos de agrupamento diferentes.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Muitas vezes denotado <em>R<\/em> , o \u00edndice Rand \u00e9 calculado da seguinte forma:<\/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;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>a:<\/strong> o n\u00famero de vezes que um par de elementos pertence ao mesmo cluster de acordo com dois m\u00e9todos de agrupamento.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b:<\/strong> o n\u00famero de vezes que um par de elementos pertence a clusters de diferen\u00e7a de acordo com dois m\u00e9todos de clustering.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n<\/sub> C <sub>2<\/sub> :<\/strong> O n\u00famero de pares n\u00e3o ordenados em um conjunto de <em>n<\/em> elementos.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O \u00edndice Rand sempre assume um valor entre 0 e 1 onde:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>0:<\/strong> indica que dois m\u00e9todos de agrupamento n\u00e3o concordam com o agrupamento de um par de elementos.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>1:<\/strong> Indica que dois m\u00e9todos de agrupamento concordam perfeitamente no agrupamento de cada par de elementos.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O exemplo a seguir ilustra como calcular o \u00edndice Rand entre dois m\u00e9todos de cluster para um conjunto de dados simples.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo: Como calcular o \u00edndice Rand<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que temos o seguinte conjunto de dados composto por cinco elementos:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Conjunto de dados: {A, B, C, D, E}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">E suponha que usemos dois m\u00e9todos de agrupamento que colocam cada elemento nos seguintes agrupamentos:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Clusters do M\u00e9todo 1: {1, 1, 1, 2, 2}<\/span><\/li>\n<li> <span style=\"color: #000000;\">M\u00e9todo de cluster 2: {1, 1, 2, 2, 3}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Para calcular o \u00edndice Rand entre esses m\u00e9todos de agrupamento, primeiro precisamos anotar todos os pares n\u00e3o ordenados poss\u00edveis no conjunto de dados de cinco elementos:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Pares n\u00e3o ordenados: {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;\">Existem <strong>10<\/strong> pares n\u00e3o ordenados.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A seguir, precisamos calcular <strong>a<\/strong> , que representa o n\u00famero de pares n\u00e3o ordenados pertencentes ao mesmo cluster em ambos os m\u00e9todos de agrupamento:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">{AB}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Neste caso, a = <strong>1<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">A seguir, precisamos calcular <strong>b<\/strong> , que representa o n\u00famero de pares n\u00e3o ordenados pertencentes a diferentes clusters nos dois m\u00e9todos de agrupamento:<\/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;\">Neste caso, b = <strong>5<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Finalmente, podemos calcular o \u00edndice Rand da seguinte forma:<\/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;\">O \u00edndice Rand \u00e9 <strong>0,6<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Como calcular o \u00edndice Rand em R<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Podemos usar a fun\u00e7\u00e3o <strong>rand.index()<\/strong> do pacote <strong>fossil<\/strong> para calcular o \u00edndice Rand entre dois m\u00e9todos de agrupamento em 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;\">O \u00edndice Rand \u00e9 <strong>0,6<\/strong> . Isso corresponde ao valor que calculamos manualmente.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Como calcular o \u00edndice Rand em Python<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Podemos definir a seguinte fun\u00e7\u00e3o em Python para calcular o \u00edndice Rand entre dois clusters:<\/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;\">O \u00edndice Rand acabou sendo <strong>0,6<\/strong> . Isto corresponde ao valor calculado nos exemplos anteriores.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pt\/k-significa-agrupamento-em-r\/\" target=\"_blank\" rel=\"noopener\">Uma introdu\u00e7\u00e3o ao agrupamento K-Means<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/k-medoides-em-r\/\" target=\"_blank\" rel=\"noopener\">Uma introdu\u00e7\u00e3o ao cluster K-Medoids<\/a><br \/> Uma introdu\u00e7\u00e3o ao cluster hier\u00e1rquico<\/p>\n","protected":false},"excerpt":{"rendered":"<p>O \u00edndice Rand \u00e9 uma forma de comparar a similaridade de resultados entre dois m\u00e9todos de agrupamento diferentes. Muitas vezes denotado R , o \u00edndice Rand \u00e9 calculado da seguinte forma: R = (a+b) \/ ( n C 2 ) Ouro: a: o n\u00famero de vezes que um par de elementos pertence ao mesmo 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":[],"class_list":["post-1642","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>O que \u00e9 o \u00cdndice Rand? 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