{"id":8281,"date":"2020-03-27T11:51:31","date_gmt":"2020-03-27T10:51:31","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=8281"},"modified":"2022-12-03T23:04:43","modified_gmt":"2022-12-03T22:04:43","slug":"minkowski-pour-les-attributs-numeriques","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/data-partitioning\/minkowski-for-numeric-attributes\/","title":{"rendered":"Minkowski for numeric attributes"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"8281\" class=\"elementor elementor-8281\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c264ecf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c264ecf\" 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-33 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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-2b814f0c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2b814f0c\" 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-158d6733\" data-id=\"158d6733\" 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 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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\/minkowski-for-numeric-attributes\/#Minkowski-pour-les-attributs-numeriques\" >Minkowski for numeric attributes<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Minkowski-pour-les-attributs-numeriques\"><\/span>Minkowski for numeric 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 Minkowski for numeric 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=\"Minkowski for numeric attributes\" width=\"389\" height=\"84\" title=\"\"><\/figure>\n\n<p>Given two instances of dimension p, x_i = (x_i1, x_i2,\u2026, X_ip) and x_j = (x_j1, x_2,\u2026, X_jp), the distance between the two data instances can be calculated using the metric by Minkowski:<\/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\/mesure2.png\" alt=\"Minkowski for numeric attributes\" width=\"506\" height=\"48\" title=\"\"><\/figure>\n\n<p>The Euclidean distance commonly used between two objects is reached when g = 2. Given g = 1, the sum of the absolute paraxial distances (Manhattan metric) is obtained, and with g = \u221e we obtain the greatest of the paraxial distances (metric of Chebychev).<\/p>\n\n<p>The unit of measurement used can affect the clustering analysis. To avoid being dependent on the choice of units of measure, the data should be normalized. Standardization of measures attempts to give all variables equal weight. However, if each variable is assigned a weight according to its importance, the weighted distance can be calculated as follows:<\/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\/mesure3.png\" alt=\"Minkowski for numeric attributes\" width=\"568\" height=\"70\" title=\"\"><\/figure>\n\n<p>\u00a0<\/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 Minkowski Wiki Home Page for Numerical Attributes Many partitioning methods use distance measures to determine similarity\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-8281","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8281","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=8281"}],"version-history":[{"count":7,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8281\/revisions"}],"predecessor-version":[{"id":18971,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8281\/revisions\/18971"}],"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=8281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}