{"id":8295,"date":"2020-03-27T11:59:29","date_gmt":"2020-03-27T10:59:29","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=8295"},"modified":"2022-12-03T23:04:44","modified_gmt":"2022-12-03T22:04:44","slug":"mesures-de-distance-pour-les-attributs-binaires","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/data-partitioning\/distance-measures-for-binary-attributes\/","title":{"rendered":"Distance measurements for binary attributes"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"8295\" class=\"elementor elementor-8295\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2c81673 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2c81673\" 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 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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-binary-attributes\/#Mesures-de-distance-pour-les-attributs-binaires\" >Distance measurements for binary attributes<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Mesures-de-distance-pour-les-attributs-binaires\"><\/span>Distance measurements for binary 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 binary 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 binary attributes\" width=\"389\" height=\"84\" title=\"\"><\/figure>\n\n<p>In the case of binary attributes, the distance between objects can be calculated based on a contingency table. A binary attribute is symmetrical if its two states have the same value. In this case, using the simple matching coefficient can assess the dissimilarity between two objects:<\/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\/mesure4.png\" alt=\"Distance measurements for binary attributes\" width=\"223\" height=\"52\" title=\"\"><\/figure>\n\n<p>where q is the number of attributes equal to 1 for the two objects; t is the number of attributes equal to 0 for the two objects; and s and r are the number of attributes that are unequal for the two objects.<\/p>\n\n<p>A binary attribute is asymmetric, if its states are not equally important (the positive result is generally considered more important). In this case, the denominator ignores unimportant negative matches (t). This is called the coefficient of <a href=\"https:\/\/complex-systems-ai.com\/en\/data-partitioning\/similarity-function\/\">Jaccard<\/a> :<\/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\/mesure5.png\" alt=\"Distance measurements for binary attributes\" width=\"179\" height=\"48\" title=\"\"><\/figure>\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 Binary 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-8295","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8295","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=8295"}],"version-history":[{"count":8,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8295\/revisions"}],"predecessor-version":[{"id":18974,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8295\/revisions\/18974"}],"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=8295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}