{
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    "date": "2024-09-05T10:17:05",
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    "modified": "2026-06-22T14:29:52",
    "modified_gmt": "2026-06-22T14:29:52",
    "slug": "insurance-analytics-with-clustering-techniques",
    "status": "publish",
    "type": "post",
    "link": "https:\/\/detralytics.com\/en\/publications\/insurance-analytics-with-clustering-techniques\/",
    "title": {
        "rendered": "Insurance Analytics with Clustering Techniques"
    },
    "content": {
        "rendered": "<div data-elementor-type=\"wp-post\" data-elementor-id=\"4029\" class=\"elementor elementor-4029\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4490deb e-flex e-con-boxed e-con e-parent\" data-id=\"4490deb\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;shape_divider_bottom&quot;:&quot;tilt&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewbox=\"0 0 1000 100\" preserveaspectratio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M0,6V0h1000v100L0,6z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e0ff49e elementor-widget elementor-widget-heading\" data-id=\"e0ff49e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Insurance Analytics with Clustering Techniques<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-37f1e74 elementor-widget elementor-widget-heading\" data-id=\"37f1e74\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">DetraNote 2020-3<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-87f3931 e-flex e-con-boxed e-con e-parent\" data-id=\"87f3931\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-9aa7e1d e-con-full e-flex e-con e-child\" data-id=\"9aa7e1d\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-67f934f elementor-widget elementor-widget-image\" data-id=\"67f934f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.mdpi.com\/2227-9091\/12\/9\/141\" target=\"_blank\">\n\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"765\" height=\"1080\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2024\/09\/Cover-Detra-Note-_Insurance-Analytics-with-Clustering-Techniques-765x1080.png\" class=\"elementor-animation-grow attachment-thumbnail size-thumbnail wp-image-5338\" alt=\"\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2024\/09\/Cover-Detra-Note-_Insurance-Analytics-with-Clustering-Techniques-765x1080.png 765w, https:\/\/detralytics.com\/wp-content\/uploads\/2024\/09\/Cover-Detra-Note-_Insurance-Analytics-with-Clustering-Techniques-768x1085.png 768w, https:\/\/detralytics.com\/wp-content\/uploads\/2024\/09\/Cover-Detra-Note-_Insurance-Analytics-with-Clustering-Techniques.png 892w\" sizes=\"(max-width: 765px) 100vw, 765px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-420ffe4 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"420ffe4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/www.mdpi.com\/2227-9091\/12\/9\/141\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon\">\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-far-arrow-alt-circle-down\" viewbox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M256 8C119 8 8 119 8 256s111 248 248 248 248-111 248-248S393 8 256 8zm0 448c-110.5 0-200-89.5-200-200S145.5 56 256 56s200 89.5 200 200-89.5 200-200 200zm-32-316v116h-67c-10.7 0-16 12.9-8.5 20.5l99 99c4.7 4.7 12.3 4.7 17 0l99-99c7.6-7.6 2.2-20.5-8.5-20.5h-67V140c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12z\"><\/path><\/svg>\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Read here<\/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<\/div>\n\t\t<div class=\"elementor-element elementor-element-2e62cc6 e-con-full e-flex e-con e-child\" data-id=\"2e62cc6\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fc5d00b elementor-widget elementor-widget-heading\" data-id=\"fc5d00b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f1e1dc7 elementor-widget elementor-widget-text-editor\" data-id=\"f1e1dc7\" 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<p>The k-means algorithm and its variants are popular techniques of clustering. Their purpose is to uncover group structures in a dataset. In actuarial applications, these methods detect clusters of policies with similar features and allows to draw a map of dominant risks. This working note starts with a review of the k-means algorithm and develops next two extensions to manage categorical features. We develop a mini-batch version that keeps computation time under control when analysing a high-dimensional dataset. We next introduce the fuzzy k-means in which policies can belong to multiple clusters. Finally, we conclude by a detailed introduction to spectral clustering.<\/p>\n<p><strong><span style=\"color: #097566;\">Keywords: <\/span><\/strong>Clustering analysis, unsupervised learning, k-means, spectral clustering.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0f29719 e-con-full e-flex e-con e-child\" data-id=\"0f29719\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2952de9 elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"2952de9\" 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<p><b>Sector: <\/b>Insurance<\/p>\n<p><b><\/b><b>Expertise: <\/b>Machine learning<\/p>\n<p><b>Authors:<\/b>\u00a0Charlotte Jamotton,<\/p>\n<p>Donatien Hainaut, and Thomas Hames<\/p>\n<p>\u00a0<\/p>\n<p><b>\u00a0<\/b><\/p>\n<p><b>Publication:<\/b> Risks<\/p>\n<p><b>Date:<\/b> September 2024<\/p>\n<p><b>Language:<\/b> English<\/p>\n<p><b>Pages:<\/b> 28<\/p>\n<p>\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c6ae38d e-flex e-con-boxed e-con e-parent\" data-id=\"c6ae38d\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a1c05c2 elementor-widget elementor-widget-spacer\" data-id=\"a1c05c2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f183faa elementor-widget elementor-widget-heading\" data-id=\"f183faa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">About the authors<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-911526c e-flex e-con-boxed e-con e-parent\" data-id=\"911526c\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-ceadb54 e-con-full e-flex e-con e-child\" data-id=\"ceadb54\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-821e45b elementor-widget elementor-widget-image\" data-id=\"821e45b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"800\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond.jpg\" class=\"attachment-large size-large wp-image-2876\" alt=\"Donatien Hainaut\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond.jpg 1042w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-768x768.jpg 768w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-146x146.jpg 146w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-50x50.jpg 50w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-75x75.jpg 75w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-85x85.jpg 85w, https:\/\/detralytics.com\/wp-content\/uploads\/2023\/07\/Donatien_Rond-80x80.jpg 80w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2dd444c e-con-full e-flex e-con e-child\" data-id=\"2dd444c\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-99d0106 elementor-widget elementor-widget-heading\" data-id=\"99d0106\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Donatien Hainaut<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fddcba9 elementor-widget elementor-widget-text-editor\" data-id=\"fddcba9\" 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<p class=\"has-text-color has-link-color\" style=\"color: #383838;\">Donatien Hainaut is a Scientific Advisor at Detralytics and a professor at UCLouvain (Belgium), where he serves as the Director of the Master&#8217;s program in Data Science with a statistical orientation. Prior to this, he held several academic positions, including Associate Professor at Rennes School of Business and ENSAE in Paris. He also has extensive industry experience, having worked as a Risk Officer, Quantitative Analyst, and ALM Officer.<\/p><p>   <\/p><p class=\"has-text-color has-link-color\" style=\"color: #383838;\">Donatien is a Qualified Actuary and holds a PhD in the field of Asset and Liability Management. His current research focuses on contagion mechanisms in stochastic processes and the applications of neural networks in insurance.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-53f26ef e-flex e-con-boxed e-con e-parent\" data-id=\"53f26ef\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-45ca7dd e-con-full e-flex e-con e-child\" data-id=\"45ca7dd\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d43f55d elementor-widget elementor-widget-image\" data-id=\"d43f55d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"782\" height=\"782\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2022\/01\/Thomas_rond.png\" class=\"attachment-large size-large wp-image-4324\" alt=\"\" srcset=\"https:\/\/detralytics.com\/wp-content\/uploads\/2022\/01\/Thomas_rond.png 782w, https:\/\/detralytics.com\/wp-content\/uploads\/2022\/01\/Thomas_rond-768x768.png 768w\" sizes=\"(max-width: 782px) 100vw, 782px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-f0de6fc e-con-full e-flex e-con e-child\" data-id=\"f0de6fc\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-224cb75 elementor-widget elementor-widget-heading\" data-id=\"224cb75\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Thomas Hames<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-58dff6d elementor-widget elementor-widget-text-editor\" data-id=\"58dff6d\" 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<p class=\"has-text-color has-link-color wp-elements-e1b283c50f5ac427982e336bbf0a75f2\">Since joining Detralytics in 2019, Thomas has primarily worked on pricing and reserving topics in P&amp;C retail Auto and Non-Life, combining classical methods with ML-based approaches.<\/p>\n<p class=\"has-text-color has-link-color wp-elements-d6053cf2cad6d00f30a2e72c492aa7d1\">Additionally, internally, Thomas is involved in the technical and commercial development of our micro-reserving package and ensures the monitoring and supervision of projects emerging within our Innovation Lab.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-12661e8 e-flex e-con-boxed e-con e-parent\" data-id=\"12661e8\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-c48cc01 e-con-full e-flex e-con e-child\" data-id=\"c48cc01\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3353cbc elementor-widget elementor-widget-image\" data-id=\"3353cbc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/detralytics.com\/wp-content\/uploads\/2024\/09\/user-no-face.png\" class=\"attachment-large size-large wp-image-4904\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d423f44 e-con-full e-flex e-con e-child\" data-id=\"d423f44\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a42dc88 elementor-widget elementor-widget-heading\" data-id=\"a42dc88\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Charlotte Jamotton<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1cfdc6d elementor-widget elementor-widget-text-editor\" data-id=\"1cfdc6d\" 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<p>Charlotte is a PhD Student in Actuarial Science at UCLouvain.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-646136e e-flex e-con-boxed e-con e-parent\" data-id=\"646136e\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fa413a6 elementor-widget elementor-widget-button\" data-id=\"fa413a6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/detralytics.com\/en\/publications\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon\">\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-arrow-left\" viewbox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M257.5 445.1l-22.2 22.2c-9.4 9.4-24.6 9.4-33.9 0L7 273c-9.4-9.4-9.4-24.6 0-33.9L201.4 44.7c9.4-9.4 24.6-9.4 33.9 0l22.2 22.2c9.5 9.5 9.3 25-.4 34.3L136.6 216H424c13.3 0 24 10.7 24 24v32c0 13.3-10.7 24-24 24H136.6l120.5 114.8c9.8 9.3 10 24.8.4 34.3z\"><\/path><\/svg>\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">All Publications<\/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\t\t<\/div>\n\t\t\t\t<\/div>",
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        "rendered": "<p>This working note starts with a review of the k-means algorithm and develops next two extensions to manage categorical features. <\/p>",
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