{"id":200,"date":"2023-05-30T08:55:23","date_gmt":"2023-05-30T08:55:23","guid":{"rendered":"http:\/\/math-in.net\/9imw\/?page_id=200"},"modified":"2023-06-06T11:54:15","modified_gmt":"2023-06-06T11:54:15","slug":"problem-3","status":"publish","type":"page","link":"https:\/\/math-in.net\/9imw\/en\/problem-3\/","title":{"rendered":"Problem 3"},"content":{"rendered":"<h4>Problem 3<\/h4>\n<p><img class=\"alignnone size-medium wp-image-253\" src=\"http:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-300x43.png\" alt=\"\" width=\"300\" height=\"43\" srcset=\"https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-200x29.png 200w, https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-300x43.png 300w, https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-400x57.png 400w, https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-600x86.png 600w, https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-768x110.png 768w, https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-800x114.png 800w, https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-1024x146.png 1024w, https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-1200x171.png 1200w, https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS-1536x219.png 1536w, https:\/\/math-in.net\/9imw\/wp-content\/uploads\/sites\/17\/2023\/05\/IMUS.png 2208w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Challenge Title |<\/strong>Diversity in Cluster Analysis.<\/p>\n<p><strong>Brief description of the challenge:<\/strong><\/p>\n<p>In Cluster Analysis, given a data set X and a distance matrix on X, one seeks a partition of X into p subsets in such a way that elements in the same group are close from each other (and elements in different subsets are far from each other). At the same time, a representative of each group is chosen.<\/p>\n<p>Suppose a problem in which fairness is considered: we have one or\u00a0 several categorical features (in the simplest case, one binary variable), identifying sensitive issues (e.g. race, gender, nationality, etc). The prototypes selected may not be diverse enough in terms of such features.<\/p>\n<p>The challenge is to model the problem incorporating a diversity criterion for the representatives chosen. A mathematical optimization model is to be developed, and an algorithm is to be designed and implemented to address the challenge.<\/p>\n<p>Mathematical background | Students need to have basic knowledge of some programming language, basic statistics and\/or data analysis.<\/p>\n<p>&nbsp;<\/p>\n<p><strong><em>Coordinator |<\/em><\/strong><em>\u00a0Emilio Carrizosa, Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universidad de Sevilla, Espa\u00f1a<\/em><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem 3 Challenge Title |Diversity in Cluster Analysis. Brief description [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Problem 3 - IX IBERIAN MODELLING WEEK<\/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:\/\/math-in.net\/9imw\/en\/problem-3\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Problem 3 - IX IBERIAN MODELLING WEEK\" \/>\n<meta property=\"og:description\" content=\"Problem 3 Challenge Title |Diversity in Cluster Analysis. 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