{"id":8305,"date":"2020-03-27T12:07:55","date_gmt":"2020-03-27T11:07:55","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=8305"},"modified":"2022-12-03T23:04:44","modified_gmt":"2022-12-03T22:04:44","slug":"mesures-de-distance-pour-les-attributs-nominaux","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/data-partitioning\/distance-measures-for-nominal-attributes\/","title":{"rendered":"Distance measurements for nominal attributes"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"8305\" class=\"elementor elementor-8305\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4456885 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4456885\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div 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target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\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<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3bb144d2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3bb144d2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5a27b5f4\" data-id=\"5a27b5f4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-24b493ad elementor-widget elementor-widget-text-editor\" data-id=\"24b493ad\" 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\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/data-partitioning\/distance-measures-for-nominal-attributes\/#Mesures-de-distance-pour-les-attributs-nominaux\" >Distance measurements for nominal attributes<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Mesures-de-distance-pour-les-attributs-nominaux\"><\/span>Distance measurements for nominal attributes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Many methods of <a href=\"https:\/\/complex-systems-ai.com\/en\/data-partitioning\/\">partitioning<\/a> use distance measures to determine the similarity or dissimilarity between any pair of objects (like distance measures for nominal attributes). It is common to denote the distance between two instances x_i and x_j as: d(x_i, x_j). A valid distance measure must be symmetric and obtains its minimum value (usually zero) in the case of identical vectors. The distance measure is called a metric distance measure if it also satisfies the following properties:<\/p>\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" class=\"alignnone\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/mesure1.png\" alt=\"Distance measurements for nominal attributes\" width=\"389\" height=\"84\" title=\"\"><\/figure>\n\n<p>When attributes are nominal, two main approaches can be used:<\/p>\n\n<ol class=\"wp-block-list\">\n<li>Simple match<\/li>\n<\/ol>\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" class=\"alignnone\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/mesure6.png\" alt=\"Distance measurements for nominal attributes\" width=\"158\" height=\"48\" title=\"\"><\/figure>\n\n<p>where p is the total number of attributes and m is the number of matches.<\/p>\n\n<p>2. Creating a <a href=\"https:\/\/complex-systems-ai.com\/en\/data-partitioning\/distance-measures-for-binary-attributes\/\">binary attribute<\/a> for each state of each nominal attribute and calculation of their dissimilarity.<\/p>\n\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<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Data Partitioning Wiki Home Page Distance Measures for Nominal Attributes Many partitioning methods use distance measures to determine \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":8271,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-8305","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8305","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=8305"}],"version-history":[{"count":6,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8305\/revisions"}],"predecessor-version":[{"id":18975,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8305\/revisions\/18975"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8271"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=8305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}