{"id":800,"date":"2026-01-17T21:31:25","date_gmt":"2026-01-18T00:31:25","guid":{"rendered":"https:\/\/wordpress.ft.unicamp.br\/revisa\/?p=800"},"modified":"2026-01-17T21:32:08","modified_gmt":"2026-01-18T00:32:08","slug":"tutorial-simplificado-de-agrupamento-k-means","status":"publish","type":"post","link":"https:\/\/wordpress.ft.unicamp.br\/revisa\/2026\/01\/17\/tutorial-simplificado-de-agrupamento-k-means\/","title":{"rendered":"Tutorial simplificado de agrupamento: K-means"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"800\" class=\"elementor elementor-800\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4bd18ab e-flex e-con-boxed e-con e-parent\" data-id=\"4bd18ab\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1814a60 elementor-widget elementor-widget-text-editor\" data-id=\"1814a60\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">Modelos de agrupamento s\u00e3o t\u00e9cnicas de aprendizado n\u00e3o supervisionado usadas para organizar dados em grupos (clusters) de forma que elementos semelhantes fiquem no mesmo grupo e diferentes fiquem em grupos distintos. Eles s\u00e3o amplamente aplicados quando n\u00e3o h\u00e1 r\u00f3tulos ou classes pr\u00e9-definidas nos dados. O K-means \u00e9 um dos algoritmos de agrupamento mais conhecidos. Ele funciona dividindo os dados em K grupos, de acordo com a proximidade entre os pontos e os centr\u00f3ides (as m\u00e9dias de cada grupo). O processo \u00e9 repetido at\u00e9 que os centr\u00f3ides se estabilizam, ou seja, at\u00e9 a converg\u00eancia.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2b6755a e-con-full e-grid e-con e-child\" data-id=\"2b6755a\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-940eb16 elementor-widget elementor-widget-image\" data-id=\"940eb16\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"186\" height=\"300\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Inicio_K-means-Be-Like_Imagem1-186x300.png\" class=\"attachment-medium size-medium wp-image-802\" alt=\"Meme com a legenda &#039;k-means be like&#039;. A imagem mostra quatro homens dentro de uma piscina de bolinhas. Eles est\u00e3o dispostos em c\u00edrculo e usam seus bra\u00e7os e corpos para separar fisicamente as bolinhas em quatro grandes grupos de cores distintas: azul, amarelo, verde e rosa.\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Inicio_K-means-Be-Like_Imagem1-186x300.png 186w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Inicio_K-means-Be-Like_Imagem1.png 218w\" sizes=\"(max-width: 186px) 100vw, 186px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">        Imagem 1 - exemplo do processo de forma\u00e7\u00e3o de clusters<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2de4c58 elementor-widget elementor-widget-text-editor\" data-id=\"2de4c58\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">Esse modelo \u00e9 aplic\u00e1vel nas seguintes situa\u00e7\u00f5es:<\/span><\/p><ul><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">S<\/span><span style=\"font-weight: 400\">egmenta\u00e7\u00e3o de clientes em marketing;<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Agrupamento de documentos ou not\u00edcias semelhantes;<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">An\u00e1lise de padr\u00f5es em dados de sa\u00fade, sensores ou redes sociais;<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Detec\u00e7\u00e3o de anomalias ou comportamentos fora do padr\u00e3o.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-b68be15 e-flex e-con-boxed e-con e-parent\" data-id=\"b68be15\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-77816b5 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"77816b5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-062a5d9 elementor-widget elementor-widget-heading\" data-id=\"062a5d9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><h2 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a><i>\n\"Como esse modelo \u00e9 implementado?\"\t  <\/i> \n<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h2><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3539269 e-flex e-con-boxed e-con e-parent\" data-id=\"3539269\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-cb0288a elementor-widget elementor-widget-heading\" data-id=\"cb0288a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><h3 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a>\nImporta\u00e7\u00e3o das bibliotecas e da base de dados\n<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h3><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-411fbf0 elementor-widget elementor-widget-text-editor\" data-id=\"411fbf0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">Para iniciar tarefas de agrupamento de dados \u00e9 necess\u00e1rio importar algumas bibliotecas, para garantir o funcionamento pleno (plotagem de gr\u00e1ficos, uso de fun\u00e7\u00f5es matem\u00e1ticas). Sendo elas:\u00a0<\/span><\/p><p><b>pandas<\/b><span style=\"font-weight: 400\"> \u2192 manipula\u00e7\u00e3o de dados;\u00a0<\/span><\/p><p><b>numpy<\/b><span style=\"font-weight: 400\"> \u2192 opera\u00e7\u00f5es matem\u00e1ticas;\u00a0<\/span><\/p><p><b>matplotlib<\/b><span style=\"font-weight: 400\"> \u2192 visualiza\u00e7\u00e3o gr\u00e1fica;<\/span><b>\u00a0<\/b><\/p><p><b>KMeans<\/b><span style=\"font-weight: 400\"> \u2192 algoritmo de agrupamento;\u00a0<\/span><\/p><p><b>StandardScaler <\/b><span style=\"font-weight: 400\">\u2192 normaliza\u00e7\u00e3o;\u00a0<\/span><\/p><p><b>train_test_split<\/b><span style=\"font-weight: 400\"> \u2192 separa\u00e7\u00e3o de conjuntos de treino e teste<\/span><span style=\"font-weight: 400\">\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-48027ec elementor-widget elementor-widget-image\" data-id=\"48027ec\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"640\" height=\"330\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao1_Codigo_Imagem1-1024x528.png\" class=\"attachment-large size-large wp-image-803\" alt=\"\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao1_Codigo_Imagem1-1024x528.png 1024w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao1_Codigo_Imagem1-300x155.png 300w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao1_Codigo_Imagem1-768x396.png 768w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao1_Codigo_Imagem1.png 1213w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Imagem 2 - imagem mostrando as bibliotecas a cria\u00e7\u00e3o do dataFrame no colab<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-aaa933f e-flex e-con-boxed e-con e-parent\" data-id=\"aaa933f\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-867de5f elementor-widget elementor-widget-heading\" data-id=\"867de5f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><h3 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a>\nPr\u00e9-processamento, limpeza, integra\u00e7\u00e3o e transforma\u00e7\u00e3o\n\n<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h3><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9332e82 e-flex e-con-boxed e-con e-parent\" data-id=\"9332e82\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-301109e elementor-widget elementor-widget-text-editor\" data-id=\"301109e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">Com a etapa de limpeza e pr\u00e9-processamento garantimos a qualidade dos dados antes da minera\u00e7\u00e3o. Consiste em identificar e tratar valores ausentes, usando t\u00e9cnicas como imputa\u00e7\u00e3o pela m\u00e9dia, moda ou por similaridade, al\u00e9m de corrigir inconsist\u00eancias causadas por erros de digita\u00e7\u00e3o ou padroniza\u00e7\u00e3o entre sistemas.\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3c17d7f elementor-widget elementor-widget-image\" data-id=\"3c17d7f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"263\" height=\"300\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao2_OrdemExemplo_imagem1-1-263x300.png\" class=\"attachment-medium size-medium wp-image-806\" alt=\"Diagrama de fluxo vertical composto por cinco blocos azuis empilhados, ilustrando a sequ\u00eancia l\u00f3gica de desenvolvimento de um projeto de Aprendizado de M\u00e1quina, iniciando na defini\u00e7\u00e3o do problema e terminando na avalia\u00e7\u00e3o do modelo.\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao2_OrdemExemplo_imagem1-1-263x300.png 263w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao2_OrdemExemplo_imagem1-1.png 756w\" sizes=\"(max-width: 263px) 100vw, 263px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">\t\t\t   Imagem 3 - etapas principais de um projeto de machine learning<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fc9b8c3 elementor-widget elementor-widget-text-editor\" data-id=\"fc9b8c3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">Tamb\u00e9m envolve a integra\u00e7\u00e3o de dados de diferentes fontes e a transforma\u00e7\u00e3o para uniformizar formatos, capitaliza\u00e7\u00e3o e unidades. Esse processo torna o conjunto de dados coerente, confi\u00e1vel e pronto para o agrupamento. Algumas opera\u00e7\u00f5es que podem ser aplicadas a essa etapa s\u00e3o:\u00a0<\/span><\/p><ul><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Dicion\u00e1rio para substitui\u00e7\u00e3o de dados faltantes<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Verifica\u00e7\u00e3o de valores nulos<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Verifica\u00e7\u00e3o de outliers (remo\u00e7\u00e3o ou n\u00e3o)<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Normaliza\u00e7\u00e3o de valores num\u00e9ricos<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Convers\u00e3o de dados (exemplo: One hot enconding)<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8d5e4f1 elementor-widget elementor-widget-image\" data-id=\"8d5e4f1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"178\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao2_Codigo_imagem2.png\" class=\"attachment-large size-large wp-image-807\" alt=\"\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao2_Codigo_imagem2.png 895w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao2_Codigo_imagem2-300x83.png 300w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao2_Codigo_imagem2-768x214.png 768w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Imagem 4 - Remo\u00e7\u00e3o de dados duplicados e Normaliza\u00e7\u00e3o de vari\u00e1veis num\u00e9ricas<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bcf8faa elementor-widget elementor-widget-heading\" data-id=\"bcf8faa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><h3 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a>\nVari\u00e1veis relevantes e treino do modelo\n<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h3><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3d279d4 elementor-widget elementor-widget-text-editor\" data-id=\"3d279d4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">\u00c9 importante selecionar as vari\u00e1veis para garantir que o modelo use apenas os atributos mais relevantes, evitando ru\u00eddo e melhorando o desempenho. Reduzindo a complexidade, aumentando a precis\u00e3o e facilitando a interpreta\u00e7\u00e3o dos resultados. Pode ser feita com base em an\u00e1lise estat\u00edstica, m\u00e9todos autom\u00e1ticos (como <\/span><i><span style=\"font-weight: 400\">feature selection<\/span><\/i><span style=\"font-weight: 400\"> do scikit-learn) ou conhecimento do dom\u00ednio, escolhendo as vari\u00e1veis que realmente influenciam o problema.<\/span><\/p><p><span style=\"font-weight: 400\">Para executar o agrupamento, utilizamos apenas as vari\u00e1veis num\u00e9ricas relevantes para o problema e ajustamos o modelo K-means com K grupos.<\/span><\/p><p><span style=\"font-weight: 400\">O valor de K deve ser escolhido com base em m\u00e9todos como o cotovelo (Elbow) ou o coeficiente de silhueta, e n\u00e3o apenas por ser menor que o n\u00famero de amostras \u2014 embora, naturalmente, K n\u00e3o possa exceder o n\u00famero total de observa\u00e7\u00f5es (K \u2264 n).<\/span><\/p><p><span style=\"font-weight: 400\">Dentro do conjunto de treino s\u00e3o realizadas as seguintes etapas para formar os grupos e ajustar o algoritmo:<\/span><\/p><ul><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">k \u00e9 escolhido pelo usu\u00e1rio;<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Cada ponto da massa de dados \u00e9 atribu\u00eddo ao centr\u00f3ide mais pr\u00f3ximo;<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">A atribui\u00e7\u00e3o \u00e9 feita de Se\u00e7\u00e3o3_GifResultados_Imagem1acordo com uma medida de dist\u00e2ncia;<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Cada cole\u00e7\u00e3o de pontos atribu\u00eddos a um centr\u00f3ide \u00e9 um grupo;<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">O centr\u00f3ide (c\u00e1lculo da nova m\u00e9dia) \u00e9 atualizado refazendo-se as medidas de dist\u00e2ncia no pr\u00f3prio grupo;<\/span><\/li><li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Os passos s\u00e3o repetidos at\u00e9 que o centr\u00f3ide de cada grupo permane\u00e7a est\u00e1vel, ou seja, nenhum objeto \u00e9 trocado de grupo.<\/span><\/li><\/ul><p>\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7589dba elementor-widget elementor-widget-image\" data-id=\"7589dba\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"384\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao3_GifResultados_Imagem1.gif\" class=\"attachment-large size-large wp-image-808\" alt=\"Anima\u00e7\u00e3o de um gr\u00e1fico de dispers\u00e3o mostrando o processo de itera\u00e7\u00e3o do algoritmo K-Means. O gr\u00e1fico exibe tr\u00eas grupos de dados sendo classificados em regi\u00f5es coloridas (vermelho, azul e verde) \u00e0 medida que os centroides (marcadores amarelos) se ajustam para encontrar o centro ideal de cada grupo.\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">V\u00eddeo 1 - primeira itera\u00e7\u00e3o de um algoritmo de k-means, onde os pontos de dados est\u00e3o sendo atribu\u00eddos aos clusters iniciais.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-902a0ad elementor-widget elementor-widget-text-editor\" data-id=\"902a0ad\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>A partir dos resultados obtidos, conseguimos agrupar da melhor maneira, conforme as itera\u00e7\u00f5es ocorrem no algoritmo.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-57dc863 elementor-widget elementor-widget-image\" data-id=\"57dc863\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"576\" height=\"228\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Divisao-dos-dados-k-means.png\" class=\"attachment-large size-large wp-image-809\" alt=\"Captura de tela de um bloco de c\u00f3digo Python onde o algoritmo K-Means \u00e9 instanciado e treinado. O c\u00f3digo define a vari\u00e1vel &#039;k&#039; como 3, inicializa o modelo KMeans com esse n\u00famero de clusters e um estado aleat\u00f3rio fixo, e em seguida ajusta o modelo aos dados normalizados usando o m\u00e9todo .fit().\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Divisao-dos-dados-k-means.png 576w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Divisao-dos-dados-k-means-300x119.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">        Imagem 5 - Treinamento do algoritmo K-Means com 3 clusters nos dados normalizados.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dbbeca6 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"dbbeca6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7b3a3d0 elementor-widget elementor-widget-heading\" data-id=\"7b3a3d0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><h2 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a>\nAplicar aprendizados ao modelo de teste\t \n<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h2><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ae800a4 elementor-widget elementor-widget-text-editor\" data-id=\"ae800a4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">Ap\u00f3s o ajuste do modelo, os centr\u00f3ides obtidos podem ser utilizados para atribuir novas observa\u00e7\u00f5es ao cluster mais pr\u00f3ximo, aplicando a mesma medida de dist\u00e2ncia usada no processo de agrupamento.<\/span><\/p><p><span style=\"font-weight: 400\">Essa etapa n\u00e3o tem o objetivo de avaliar generaliza\u00e7\u00e3o, como ocorre em modelos supervisionados, mas sim de verificar a estabilidade do padr\u00e3o de agrupamento quando aplicado a dados in\u00e9ditos \u2014 isto \u00e9, observar se a estrutura formada se mant\u00e9m coerente para novos pontos.<\/span><\/p><p><span style=\"font-weight: 400\">Para avaliar a qualidade dos agrupamentos produzidos, utilizam-se m\u00e9tricas espec\u00edficas que analisam simultaneamente a coer\u00eancia interna dos clusters (o qu\u00e3o pr\u00f3ximos os pontos de um mesmo grupo est\u00e3o entre si) e a separa\u00e7\u00e3o entre clusters (o qu\u00e3o distintos os grupos s\u00e3o no espa\u00e7o).<\/span><\/p><p><span style=\"font-weight: 400\">Entre as m\u00e9tricas mais utilizadas est\u00e3o:<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7d35412 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"7d35412\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2c20b6c elementor-widget elementor-widget-heading\" data-id=\"2c20b6c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><h3 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a>\nCoeficiente de Silhueta (Silhouette Score):\n<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h3><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21a988c elementor-widget elementor-widget-text-editor\" data-id=\"21a988c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">\u00a0mede o qu\u00e3o bem cada ponto est\u00e1 alocado ao seu grupo \u2014 valores pr\u00f3ximos de 1 indicam boa separa\u00e7\u00e3o.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-676d6d1 elementor-widget elementor-widget-image\" data-id=\"676d6d1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"115\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Coeficiente_Silhouette_Imagem1-300x115.png\" class=\"attachment-medium size-medium wp-image-810\" alt=\"F\u00f3rmula do coeficiente de Silhueta\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Coeficiente_Silhouette_Imagem1-300x115.png 300w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Coeficiente_Silhouette_Imagem1.png 398w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">\t\t\tImagem 6 - F\u00f3rmula do Coeficiente de Silhueta<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9fd22e0 elementor-widget elementor-widget-text-editor\" data-id=\"9fd22e0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Como \u00e9 calculado?<\/b><\/p><p><span style=\"font-weight: 400\"> Na f\u00f3rmula n\u00f3s temos os termos b(i) que representa o valor de separa\u00e7\u00e3o, ou seja, \u00e9 a dist\u00e2ncia m\u00e9dia entre um ponto de dados \u2018i\u2019 e os pontos em qualquer outro cluster. J\u00e1 a(i) representa a coes\u00e3o,\u00a0 a <\/span><b>dist\u00e2ncia m\u00e9dia<\/b><span style=\"font-weight: 400\"> entre o ponto de dado\u00a0 e todos os outros pontos no <\/span><b>mesmo cluster.<\/b><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8fd16e5 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"8fd16e5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-761fc35 elementor-widget elementor-widget-heading\" data-id=\"761fc35\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><h3 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a>\n\u00cdndice de Davies-Bouldin (DBI):\n<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h3><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0de3c8b elementor-widget elementor-widget-heading\" data-id=\"0de3c8b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><h3 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a>\n\u00cdndice de Davies-Bouldin (DBI):\n<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h3><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b5274af elementor-widget elementor-widget-text-editor\" data-id=\"b5274af\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">Avalia a compacidade e separa\u00e7\u00e3o dos clusters \u2014 quanto menor o valor, melhor o agrupamento.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4ba8450 elementor-widget elementor-widget-image\" data-id=\"4ba8450\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"162\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Davies-Bouldin_Imagem2-300x162.png\" class=\"attachment-medium size-medium wp-image-811\" alt=\"\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Davies-Bouldin_Imagem2-300x162.png 300w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Davies-Bouldin_Imagem2.png 349w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">  Imagem 7 - M\u00e9trica para avalia\u00e7\u00e3o de qualidade de clusters.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7726dc3 elementor-widget elementor-widget-text-editor\" data-id=\"7726dc3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Como \u00e9 calculado?<\/b><\/p><p><span style=\"font-weight: 400\">Para calcular o <\/span><b>\u00cdndice de Davies-Bouldin (DBI) <\/b><span style=\"font-weight: 400\">\u00e9 necess\u00e1rio conhecer a similaridade m\u00e1xima de todos os cluster i em rela\u00e7\u00e3o aos cluster existentes, assim \u00e9 poss\u00edvel fazer a m\u00e9dia das similaridades. A medida de similaridade entre dois clusters \u00e9 a raz\u00e3o da soma de suas dispers\u00f5es individuais pela dist\u00e2ncia entre seus centr\u00f3ides. Portanto, \u00e9 necess\u00e1rio\u00a0 calcular tamb\u00e9m a dispers\u00e3o Intra-Cluster, que \u00e9 a m\u00e9dia da dist\u00e2ncia de cada ponto de dado de um cluster em rela\u00e7\u00e3o ao centr\u00f3ide, e a separa\u00e7\u00e3o Inter-Cluster, que \u00e9 a dist\u00e2ncia entre centr\u00f3ides.\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-80572bd e-grid e-con-full e-con e-child\" data-id=\"80572bd\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1e7f833 elementor-widget elementor-widget-image\" data-id=\"1e7f833\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"101\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Davies-Bouldin_Inter-Cluster_Imagem3.png\" class=\"attachment-large size-large wp-image-812\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Imagem 8 - F\u00f3rmula que calcula a dispers\u00e3o m\u00e9dia dos pontos dentro de um cluster <\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6d48a21 elementor-widget elementor-widget-image\" data-id=\"6d48a21\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"84\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Davies-Bouldin_Intra-Cluster_Imagem4.png\" class=\"attachment-large size-large wp-image-813\" alt=\"\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Davies-Bouldin_Intra-Cluster_Imagem4.png 343w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Davies-Bouldin_Intra-Cluster_Imagem4-300x73.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Imagem 9 - F\u00f3rmula que calcula a dist\u00e2ncia entre os centros de dois clusters diferentes        <\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a5386d3 e-flex e-con-boxed e-con e-parent\" data-id=\"a5386d3\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e291ecb elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"e291ecb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cdd78e2 elementor-widget elementor-widget-heading\" data-id=\"cdd78e2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><h3 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a>\n\u00cdndice Calinski-Harabasz (CH)<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h3><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4a6b170 elementor-widget elementor-widget-text-editor\" data-id=\"4a6b170\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400\">mede a raz\u00e3o entre dispers\u00e3o entre e dentro dos grupos \u2014 valores maiores indicam melhor defini\u00e7\u00e3o dos clusters.<\/span><span style=\"font-weight: 400\"><br \/><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-03a9ec1 elementor-widget elementor-widget-image\" data-id=\"03a9ec1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"99\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/Secao4_Calinski-Harabasz_Imagem5.png\" class=\"attachment-medium size-medium wp-image-820\" alt=\"Equa\u00e7\u00e3o matem\u00e1tica para o c\u00e1lculo do \u00cdndice Calinski-Harabasz (CH). A f\u00f3rmula \u00e9 uma fra\u00e7\u00e3o onde o numerador representa a dispers\u00e3o entre grupos ($SS_B$ dividido por $K - 1$) e o denominador representa a dispers\u00e3o dentro dos grupos ($SS_W$ dividido por $N - K$).\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Imagem 10 - F\u00f3rmula do \u00cdndice Calinski-Harabasz - mede a qualidade da divis\u00e3o em clusters.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dbc8cfd elementor-widget elementor-widget-text-editor\" data-id=\"dbc8cfd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Como \u00e9 calculado?<\/b><\/p><p><span style=\"font-weight: 400\">A partir da defini\u00e7\u00e3o de um centr\u00f3ide global, ou seja, a m\u00e9dia das amostras no conjunto de dados, \u00e9 poss\u00edvel calcular o SSb que \u00e9 a dist\u00e2ncia quadrada entre o centr\u00f3ide do cluster e a m\u00e9dia global, ponderada pelo n\u00famero de pontos no cluster. J\u00e1 o SSw \u00e9 a dist\u00e2ncia quadrada entre os pontos e o centr\u00f3ide do seu pr\u00f3prio cluster.<\/span><\/p><p><span style=\"font-weight: 400\">Essas m\u00e9tricas auxiliam na compara\u00e7\u00e3o entre diferentes valores de K e na escolha do modelo mais adequado ao problema.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-374b1c8 elementor-widget elementor-widget-image\" data-id=\"374b1c8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"346\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/codigo_clustering_kmeans.png\" class=\"attachment-large size-large wp-image-827\" alt=\"\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/codigo_clustering_kmeans.png 935w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/codigo_clustering_kmeans-300x162.png 300w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/codigo_clustering_kmeans-768x415.png 768w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Imagem 11 - visualiza\u00e7\u00e3o dos grupos de clientes e avalia\u00e7\u00e3o com 3 m\u00e9tricas<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-687b0a0 elementor-widget elementor-widget-image\" data-id=\"687b0a0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"569\" src=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/resultados_clustering_clientes.png\" class=\"attachment-large size-large wp-image-828\" alt=\"Gr\u00e1fico de dispers\u00e3o intitulado &#039;Agrupamento de Clientes (K-Means)&#039;. O gr\u00e1fico exibe pontos de dados distribu\u00eddos em tr\u00eas grupos distintos (amarelo, verde e roxo) baseados nos eixos de &#039;Idade&#039; e &#039;Renda Mensal&#039;. Marcadores vermelhos em forma de &#039;X&#039; indicam o centroide de cada grupo. Abaixo do gr\u00e1fico, s\u00e3o listadas as m\u00e9tricas de avalia\u00e7\u00e3o: Coeficiente de Silhueta (0.448), \u00cdndice Davies-Bouldin (0.751) e \u00cdndice Calinski-Harabasz (101.070).\" srcset=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/resultados_clustering_clientes.png 697w, https:\/\/wordpress.ft.unicamp.br\/revisa\/wp-content\/uploads\/sites\/86\/2026\/01\/resultados_clustering_clientes-300x267.png 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Imagem 12 - Resultado final do agrupamento de clientes mostrando clusters formados e suas m\u00e9tricas de avalia\u00e7\u00e3o<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4f51605 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"4f51605\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ebdc4e4 e-flex e-con-boxed e-con e-parent\" data-id=\"ebdc4e4\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-36238c0 elementor-widget elementor-widget-heading\" data-id=\"36238c0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><h2 style=\"text-indent: 0cm\"><a name=\"_w58d0z51c4at\"><\/a>\nRefer\u00eancias:<span style=\"font-family: Roboto, sans-serif;font-size: 16px\"><\/span><\/h2><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0d30ca3 elementor-widget elementor-widget-text-editor\" data-id=\"0d30ca3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>SILVA, Luiz Paulo Moreira. Dimens\u00f5es do espa\u00e7o. <\/b><b><i>Brasil Escola.<\/i><\/b><b> Dispon\u00edvel em:<\/b><a href=\"https:\/\/brasilescola.uol.com.br\/matematica\/dimensoes-espaco.htm\"> <b>https:\/\/brasilescola.uol.com.br\/matematica\/dimensoes-espaco.htm<\/b><\/a><b>. Acesso em: 14 fev. 2018.<\/b><\/p><p><b>REZENDE, Solange O.; MARCACINI, Ricardo M.; MOURA, Maria F. O uso da minera\u00e7\u00e3o de textos para extra\u00e7\u00e3o e organiza\u00e7\u00e3o n\u00e3o supervisionada de conhecimento. <\/b><b><i>Revista de Sistemas de Informa\u00e7\u00e3o da FSMA<\/i><\/b><b>, n. 7, p. 7\u201321, 2011.<\/b><\/p><p><b>NOGAR\u00c9, Diego. Entenda o algoritmo K-means. Dispon\u00edvel em:<\/b><a href=\"https:\/\/diegonogare.net\/2015\/08\/entendendo-como-funciona-o-algoritmo-de-cluster-k-means\/\"> <b>https:\/\/diegonogare.net\/2015\/08\/entendendo-como-funciona-o-algoritmo-de-cluster-k-means\/<\/b><\/a><b>. Acesso em: 5 nov. 2025.<\/b><\/p><p><b>DE CASTRO, Leandro Nunes; FERRARI, Daniel Godoy. <\/b><b><i>Introdu\u00e7\u00e3o \u00e0 Minera\u00e7\u00e3o de Dados: Conceitos B\u00e1sicos, Algoritmos e Aplica\u00e7\u00f5es.<\/i><\/b><b> S\u00e3o Paulo: Saraiva, 2016.<\/b><\/p><p><b>HAN, Jiawei; KAMBER, Micheline. <\/b><b><i>Data Mining: Concepts and Techniques.<\/i><\/b><b> 2. ed. San Francisco: Elsevier, 2006.<\/b><\/p><p><b>SCIKIT-LEARN Developers. Clustering performance evaluation. Dispon\u00edvel em:<\/b><a href=\"https:\/\/scikit-learn.org\/stable\/modules\/clustering.html#clustering-performance-evaluation\"> <b>https:\/\/scikit-learn.org\/stable\/modules\/clustering.html#clustering-performance-evaluation<\/b><\/a><b>. Acesso em: nov. 2025.<\/b><\/p><p><b>HASTIE, Trevor; TIBSHIRANI, Robert; FRIEDMAN, Jerome. <\/b><b><i>The Elements of Statistical Learning: Data Mining, Inference, and Prediction.<\/i><\/b><b> 2. ed. New York: Springer, 2009.<\/b><\/p><p><b>GOOGLE COLAB. <\/b><b><i>Notebook<\/i><\/b><b>. Dispon\u00edvel em:<\/b><a href=\"https:\/\/colab.research.google.com\/drive\/1ZmPIAhsoeGtA_WEi8qqzUXsnJpZ26Zsc#scrollTo=UUxGMy3XbSiA\"> <b>https:\/\/colab.research.google.com\/drive\/1ZmPIAhsoeGtA_WEi8qqzUXsnJpZ26Zsc#scrollTo=UUxGMy3XbSiA<\/b><\/a><b>. Acesso em: nov. 2025.<\/b><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Modelos de agrupamento s\u00e3o t\u00e9cnicas de aprendizado n\u00e3o supervisionado usadas para organizar dados em grupos (clusters) de forma que elementos semelhantes fiquem no mesmo grupo [&hellip;]<\/p>\n","protected":false},"author":125,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-800","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Tutorial simplificado de agrupamento: K-means - REVISA<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.ft.unicamp.br\/revisa\/2026\/01\/17\/tutorial-simplificado-de-agrupamento-k-means\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tutorial simplificado de agrupamento: K-means - 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