{"id":1390,"date":"2021-12-02T19:59:56","date_gmt":"2021-12-02T19:59:56","guid":{"rendered":"https:\/\/sbia.org.br\/lnlm\/?page_id=1390"},"modified":"2021-12-12T00:30:12","modified_gmt":"2021-12-12T00:30:12","slug":"vol19-no1-art1","status":"publish","type":"page","link":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/","title":{"rendered":"Improving Prototypes Representativeness by Internal Validity Index Analysis"},"content":{"rendered":"<p>Alexandre Szabo <a href=\"https:\/\/orcid.org\/0000-0002-5569-9010\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>&#038; Thomaz A. Ruckl<a href=\"https:\/\/orcid.org\/0000-0002-5740-7245\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a><\/p>\n<p><strong>Abstract:<\/strong> Internal validity indexes are applied to evaluate the solution of a partition, which no equally reflects the same quality for all clusters, individually, in terms of prototypes representativeness. Thus, knowing their representativeness in respective clusters, it is possible adjust them to increase the confidence in analysis of found clusters. In this sense, this paper proposes a simple and effective method to obtain the internal validity index value in every cluster in a partition, identify those with low prototypes representativeness and improve them. Experiments were carried out by sum of the squared error index, which measures the compactness of clusters. The behavior of the method was illustrated by a synthetic dataset and performed for ten datasets from the literature with k-Means algorithm. The results demonstrated its effectiveness for all experiments.<\/p>\n<p><strong>Keywords:<\/strong> Data clustering, internal validity index, sum of squared error, k-Means.<\/p>\n<p><strong>DOI code:<\/strong> <a href=\"http:\/\/dx.doi.org\/10.21528\/lnlm-vol19-no1-art1\">10.21528\/lnlm-vol19-no1-art1<\/a><\/p>\n<p><strong>PDF file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/12\/vol19-no1-art1.pdf\">vol19-no1-art1.pdf<\/a><\/p>\n<p><strong>BibTex file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/12\/vol19-no1-art1.bib\">vol19-no1-art1.bib<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alexandre Szabo &#038; Thomaz A. Ruckl Abstract: Internal validity indexes are applied to evaluate the solution of a partition, which no equally reflects the same quality for all clusters, individually, in terms of prototypes representativeness. Thus, knowing their representativeness in <a href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1380,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1390","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Improving Prototypes Representativeness by Internal Validity Index Analysis - Learning and NonLinear Models<\/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:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Improving Prototypes Representativeness by Internal Validity Index Analysis - Learning and NonLinear Models\" \/>\n<meta property=\"og:description\" content=\"Alexandre Szabo &#038; Thomaz A. Ruckl Abstract: Internal validity indexes are applied to evaluate the solution of a partition, which no equally reflects the same quality for all clusters, individually, in terms of prototypes representativeness. Thus, knowing their representativeness in Read More ...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/\" \/>\n<meta property=\"og:site_name\" content=\"Learning and NonLinear Models\" \/>\n<meta property=\"article:modified_time\" content=\"2021-12-12T00:30:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/\",\"name\":\"Improving Prototypes Representativeness by Internal Validity Index Analysis - Learning and NonLinear Models\",\"isPartOf\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\",\"datePublished\":\"2021-12-02T19:59:56+00:00\",\"dateModified\":\"2021-12-12T00:30:12+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/#primaryimage\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\",\"contentUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Browse issues\",\"item\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Learning &#038; Nonlinear Models &#8211; L&#038;NLM &#8211; Volume 19 &#8211; N\u00famero 1\",\"item\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Improving Prototypes Representativeness by Internal Validity Index Analysis\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#website\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/\",\"name\":\"Learning and NonLinear Models\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/sbia.org.br\/lnlm\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#organization\",\"name\":\"Learning and NonLinear Models\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png\",\"contentUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png\",\"width\":398,\"height\":94,\"caption\":\"Learning and NonLinear Models\"},\"image\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Improving Prototypes Representativeness by Internal Validity Index Analysis - Learning and NonLinear Models","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol19-no1\/vol19-no1-art1\/","og_locale":"pt_BR","og_type":"article","og_title":"Improving Prototypes Representativeness by Internal Validity Index Analysis - Learning and NonLinear Models","og_description":"Alexandre Szabo &#038; Thomaz A. 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