{"id":170439,"date":"2023-09-10T14:40:58","date_gmt":"2023-09-10T13:40:58","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=170439"},"modified":"2023-10-30T19:59:33","modified_gmt":"2023-10-30T18:59:33","slug":"k-means-clustering-in-machine-learning-a-deep-dive","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/k-means-clustering-in-machine-learning-a-deep-dive","title":{"rendered":"K-Means Clustering in Machine Learning: A Deep Dive"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"170439\" class=\"elementor elementor-170439\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-52156171 e-flex e-con-boxed e-con\" data-id=\"52156171\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1e5053af elementor-widget elementor-widget-heading\" data-id=\"1e5053af\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Clustering is a specialized discipline within Machine Learning aimed at separating your data into homogeneous groups with common characteristics. It's a highly valued field, especially in marketing, where there is often a need to segment customer databases to identify specific behaviors. The K-means algorithm is a well-known unsupervised algorithm in the realm of Clustering.<\/h2>\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2e9ebd36 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2e9ebd36\" data-element_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-3d919357\" data-id=\"3d919357\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6bb80870 elementor-widget elementor-widget-text-editor\" data-id=\"6bb80870\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>In this article, we will delve into its operation and the useful means to optimize it.<\/p><p>This algorithm was designed in 1957 at Bell Labs by Stuart P. Lloyd as a technique for pulse modulation and coding (MIC). It was only introduced to the general public in 1982. In 1965, Edward W. Forgy had already published an algorithm that was nearly identical, which is why K-means is often referred to as the <strong>Lloyd-Forgy algorithm.<\/strong><\/p><p>Its applications are diverse: customer segmentation, data analysis, image segmentation, semi-supervised learning, and more.<\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3f2affed elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3f2affed\" data-element_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-6a8778da\" data-id=\"6a8778da\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2995bc56 elementor-widget elementor-widget-heading\" data-id=\"2995bc56\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">The Principle of the K-means Algorithm<\/h3>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6979b75c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6979b75c\" data-element_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-17f2fc86\" data-id=\"17f2fc86\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4e83a1ad elementor-widget elementor-widget-text-editor\" data-id=\"4e83a1ad\" data-element_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<p><span style=\"font-weight: normal;\">Given a set of points and an integer k, the <a href=\"https:\/\/datascientest.com\/en\/algorithm-what-is-it\">algorithm<\/a> aims to divide the points into k groups, called clusters, that are homogeneous and compact. Let&#8217;s look at the example below:<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-2b831954 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2b831954\" data-element_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-50 elementor-inner-column elementor-element elementor-element-5ecc9e1c\" data-id=\"5ecc9e1c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3677334 elementor-widget elementor-widget-image\" data-id=\"3677334\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"377\" height=\"368\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans1.png\" class=\"attachment-large size-large wp-image-170443\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans1.png 377w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans1-300x293.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-2073659d\" data-id=\"2073659d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5b90fbd1 elementor-widget elementor-widget-image\" data-id=\"5b90fbd1\" data-element_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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"377\" height=\"368\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans-2.png\" class=\"attachment-large size-large wp-image-170444\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans-2.png 377w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans-2-300x293.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\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-1fcf575d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1fcf575d\" data-element_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-476862ba\" data-id=\"476862ba\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4bc151dc elementor-widget elementor-widget-text-editor\" data-id=\"4bc151dc\" data-element_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<p><span style=\"font-weight: normal;\">On this 2D dataset, it becomes clear that it can be divided into 3 groups.<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t<div class=\"elementor-element elementor-element-700dad68 e-flex e-con-boxed e-con\" data-id=\"700dad68\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-679c38c8 elementor-widget elementor-widget-heading\" data-id=\"679c38c8\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">How do we go about it?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-29fb04f elementor-widget elementor-widget-text-editor\" data-id=\"29fb04f\" data-element_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<p>The idea is quite simple and intuitive. The first step is to randomly define 3 centroids and associate them with 3 labels, for example, 0, 1, 2. Then, for each point, we calculate its distance to the 3 centroids and associate the point with the closest centroid and its corresponding label. This labels our data.<\/p><p>Finally, we recalculate 3 new centroids, which will be the centers of gravity of each labeled cluster of points. We repeat these steps until the new centroids no longer move from the previous ones. The final result is shown in the figure on the right.<\/p>\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-40250c13 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"40250c13\" data-element_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-25843c12\" data-id=\"25843c12\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-afd4b3e elementor-widget elementor-widget-heading\" data-id=\"afd4b3e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Concept of distance and initialisation<\/h3>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3c9c5b44 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3c9c5b44\" data-element_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-3aebb867\" data-id=\"3aebb867\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-32bc3b2d elementor-widget elementor-widget-text-editor\" data-id=\"32bc3b2d\" data-element_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<p>You&#8217;ve understood that in this algorithm, two key points are: What metric is used to evaluate the distance between points and centroids? What is the number of clusters to choose?<\/p><p>In the k-means algorithm, the Euclidean distance is generally used, where p = (p1,&#8230;,pn) and q = (q1,&#8230;,qn).<\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5e44cdb1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5e44cdb1\" data-element_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-3cfec997\" data-id=\"3cfec997\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5182a7eb elementor-widget elementor-widget-image\" data-id=\"5182a7eb\" data-element_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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"766\" height=\"77\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans3.png\" class=\"attachment-large size-large wp-image-170445\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans3.png 766w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans3-300x30.png 300w\" sizes=\"(max-width: 766px) 100vw, 766px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2d672b91 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2d672b91\" data-element_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-631266cd\" data-id=\"631266cd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4b190fa2 elementor-widget elementor-widget-text-editor\" data-id=\"4b190fa2\" data-element_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<p>It allows you to assess the distance between each point and the centroids. For each point, we calculate the <strong>Euclidean distance<\/strong> between that point and each of the centroids, then associate it with the closest centroid, which is the one with the smallest distance.<\/p><p>In the previous example, it was easy to find the ideal number of clusters by visualizing it graphically. Generally, datasets have more than two dimensions, making it difficult to visualize the point cloud and quickly identify the optimal number of clusters. Let&#8217;s assume in the previous example that we didn&#8217;t visualize the data beforehand and decided to test it several times with different initial numbers of clusters. Here are the results obtained:<\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4b51e7e2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4b51e7e2\" data-element_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-69bfe4f4\" data-id=\"69bfe4f4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-49d46292 elementor-widget elementor-widget-image\" data-id=\"49d46292\" data-element_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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"268\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans4.png\" class=\"attachment-large size-large wp-image-170446\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans4.png 943w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans4-300x101.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans4-768x257.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7484eabc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7484eabc\" data-element_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-781abe9a\" data-id=\"781abe9a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6a3e06ba elementor-widget elementor-widget-text-editor\" data-id=\"6a3e06ba\" data-element_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<p>The partitioning is inaccurate because the initial number of clusters is much higher than the ideal number, which in this case is 3. There are methods to determine the ideal number of clusters. The most well-known one is the elbow method. It relies on the concept of inertia, which is defined as follows: the sum of the <strong>Euclidean distances<\/strong> between each point and its associated centroid. Naturally, the higher the initial number of clusters we set, the lower the inertia becomes: points are more likely to be close to a centroid. Let&#8217;s see how this works on our example:<\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7e2f23e7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7e2f23e7\" data-element_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-7501e5c3\" data-id=\"7501e5c3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-16555d9d elementor-widget elementor-widget-image\" data-id=\"16555d9d\" data-element_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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"739\" height=\"333\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans5.png\" class=\"attachment-large size-large wp-image-170447\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans5.png 739w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans5-300x135.png 300w\" sizes=\"(max-width: 739px) 100vw, 739px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2c8478b2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2c8478b2\" data-element_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-12d76773\" data-id=\"12d76773\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-11a7129c elementor-widget elementor-widget-text-editor\" data-id=\"11a7129c\" data-element_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<p>We can see that the inertia levels off from 3 clusters. This method is conclusive. It can be coupled with a more precise but computationally intensive approach: the silhouette coefficient. It is defined as follows:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21143a4e elementor-widget elementor-widget-image\" data-id=\"21143a4e\" data-element_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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"127\" height=\"56\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/formule-kmeans.png\" class=\"attachment-large size-large wp-image-170448\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-53d34a44 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"53d34a44\" data-element_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-28a8cfbd\" data-id=\"28a8cfbd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-14e2dd02 elementor-widget elementor-widget-text-editor\" data-id=\"14e2dd02\" data-element_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<ul><li><p>a. The average distance to other observations in the same cluster (i.e., the intra-cluster average).<\/p><\/li><li><p>b. The average distance to the nearest cluster.<\/p><\/li><\/ul><p>This coefficient can vary between -1 and +1. A coefficient close to +1 means that the observation is well inside its own cluster, while a coefficient close to 0 means it is close to a boundary; finally, a coefficient close to -1 means that the observation is associated with the wrong cluster.<\/p><p>As with inertia, it is wise to display the coefficient&#8217;s evolution based on the number of clusters as shown below:<\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-aa47998 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"aa47998\" data-element_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-1418f26\" data-id=\"1418f26\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6945de3c elementor-widget elementor-widget-image\" data-id=\"6945de3c\" data-element_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=\"627\" height=\"306\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans6.png\" class=\"attachment-large size-large wp-image-170449\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans6.png 627w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans6-300x146.png 300w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/>\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\t<\/div>\n\t\t<\/div>\n\t\t\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-76bc7cf0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"76bc7cf0\" data-element_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-6d693301\" data-id=\"6d693301\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5414f17a elementor-widget elementor-widget-text-editor\" data-id=\"5414f17a\" data-element_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<p>This method also helps identify the ideal number of clusters, which in this case is 3.<\/p><p>In addition to these two methods, it is essential to conduct a detailed analysis of the created clusters. By that, I mean a precise and in-depth descriptive analysis to determine the common characteristics of each cluster. This will allow you to understand the typical profiles of each cluster.<\/p><p>\u00a0<\/p><p>\ud83d\udca1Discover also:<\/p><table dir=\"ltr\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\"><colgroup><col width=\"656\" \/><\/colgroup><tbody><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Deep Learning - All you need to know&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/all-about-deep-learning\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/all-about-deep-learning\" target=\"_blank\" rel=\"noopener\">Deep Learning &#8211; All you need to know<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Mushroom Recognition&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/mushroom-recognition\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/mushroom-recognition\" target=\"_blank\" rel=\"noopener\">Mushroom Recognition<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Tensor Flow - Google's ML&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/tensor-flow-all-about-googles-machine-learning-framework\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/tensor-flow-all-about-googles-machine-learning-framework\" target=\"_blank\" rel=\"noopener\">Tensor Flow &#8211; Google&#8217;s ML<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Dive into ML&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/unlock-your-future-dive-into-machine-learning-engineer-training\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/unlock-your-future-dive-into-machine-learning-engineer-training\" target=\"_blank\" rel=\"noopener\">Dive into ML<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Data Poisoning&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/data-poisoning-a-threat-to-machine-learning-models\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/data-poisoning-a-threat-to-machine-learning-models\" target=\"_blank\" rel=\"noopener\">Data Poisoning<\/a><\/td><\/tr><\/tbody><\/table>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-62d94ec6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"62d94ec6\" data-element_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-186c09c9\" data-id=\"186c09c9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-284ae1aa elementor-widget elementor-widget-heading\" data-id=\"284ae1aa\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">And now, the practical part in Python.<\/h3>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-67c1cc39 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"67c1cc39\" data-element_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-65545012\" data-id=\"65545012\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-76ebd097 elementor-widget elementor-widget-text-editor\" data-id=\"76ebd097\" data-element_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<p>Training a K-means algorithm is made easier with the Scikit-Learn library. Our example dataset, which was used for illustration, can be created easily using Scikit-Learn&#8217;s make_blobs function. Here&#8217;s how to implement it in code:<\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-508b1457 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"508b1457\" data-element_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-56e049d3\" data-id=\"56e049d3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7f60918a elementor-widget elementor-widget-image\" data-id=\"7f60918a\" data-element_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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"215\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans7.png\" class=\"attachment-large size-large wp-image-170450\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans7.png 943w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans7-300x81.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans7-768x207.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-773c538e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"773c538e\" data-element_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-1b2bfb59\" data-id=\"1b2bfb59\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-42d8fc7f elementor-widget elementor-widget-text-editor\" data-id=\"42d8fc7f\" data-element_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<p><span style=\"font-weight: normal;\">Now that we have our dataset, we can proceed with the implementation of K-means. We will use the Scikit-Learn library and visualize the result:<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-55985502 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"55985502\" data-element_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-5bce35f4\" data-id=\"5bce35f4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1efd2c08 elementor-widget elementor-widget-image\" data-id=\"1efd2c08\" data-element_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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"635\" height=\"383\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans8.png\" class=\"attachment-large size-large wp-image-170451\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans8.png 635w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans8-300x181.png 300w\" sizes=\"(max-width: 635px) 100vw, 635px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-331227a4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"331227a4\" data-element_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-6bcb017b\" data-id=\"6bcb017b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2c6441c2 elementor-widget elementor-widget-text-editor\" data-id=\"2c6441c2\" data-element_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<p>The `n_clusters` attribute of the<strong> Scikit-Learn&#8217;s KMeans<\/strong> class allows us to set the number of centroids we want. Therefore, it also defines the number of initial centroids.<\/p><p>By default, this class doesn&#8217;t use a random initialization method but rather a method developed in 2007 by David Arthur and Sergei Vassilvitskii called K-Means++. It involves selecting distinct centroids from each other, reducing the risk of converging to a non-optimal solution. The default distance used is, of course, the <strong>Euclidean distance defined earlier.<\/strong><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-70e723f9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"70e723f9\" data-element_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-35aebbb7\" data-id=\"35aebbb7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-276ac75 elementor-widget elementor-widget-heading\" data-id=\"276ac75\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">The limits of the k-means algorithm<\/h3>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4ba23af6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4ba23af6\" data-element_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-4411f226\" data-id=\"4411f226\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ae89f5c elementor-widget elementor-widget-text-editor\" data-id=\"ae89f5c\" data-element_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<p>Indeed, as we&#8217;ve seen, the algorithm requires defining the number of clusters beforehand. This requires having a precise idea, and even if we&#8217;ve seen two complementary methods to optimize on certain datasets, they are not infallible.<\/p><p>Indeed, datasets with elliptical shapes, for example, can pose a problem. In the example below, we clearly see two groups resembling two ellipses. The figure on the right shows the result after using the K-means algorithm. It&#8217;s evident that it failed to identify our two ellipses.<\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4599bd82 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4599bd82\" data-element_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-7e463e73\" data-id=\"7e463e73\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3886cdc2 elementor-widget elementor-widget-image\" data-id=\"3886cdc2\" data-element_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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"252\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans-9.png\" class=\"attachment-large size-large wp-image-170452\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans-9.png 943w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans-9-300x94.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/09\/kmeans-9-768x242.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-12ac16e3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"12ac16e3\" data-element_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-db8b212\" data-id=\"db8b212\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-78accd27 elementor-widget elementor-widget-text-editor\" data-id=\"78accd27\" data-element_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<p><span style=\"font-weight: normal;\">Using a clustering algorithm like the K-means algorithm is not straightforward depending on the data you have. You will often need to preprocess the data.<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t<div class=\"elementor-element elementor-element-401919b9 e-flex e-con-boxed e-con\" data-id=\"401919b9\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-368267b elementor-widget elementor-widget-text-editor\" data-id=\"368267b\" data-element_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<p>At Datascientest, we teach you how to master the main clustering algorithms and how to interpret them on datasets. Feel free to explore our training offers and apply for one of them to discover clustering as well as many other areas of <a href=\"https:\/\/datascientest.com\/en\/machine-learning-python-where-to-start\">Machine Learning.<\/a><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6f8e32e elementor-align-center button-principal elementor-widget elementor-widget-button\" data-id=\"6f8e32e\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-md\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Discover our Courses<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\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\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Clustering is a specialized discipline within Machine Learning aimed at separating your data into homogeneous groups with common characteristics. It&#8217;s a highly valued field, especially in marketing, where there is often a need to segment customer databases to identify specific behaviors. The K-means algorithm is a well-known unsupervised algorithm in the realm of Clustering. In [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":170440,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>K-Means Clustering in Machine Learning: A Deep Dive<\/title>\n<meta name=\"description\" content=\"Explore the intricacies of K-Means, a powerful clustering algorithm in Machine Learning, and unlock its potential for data ...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/en\/k-means-clustering-in-machine-learning-a-deep-dive\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"K-Means Clustering in Machine Learning: A Deep Dive\" \/>\n<meta property=\"og:description\" content=\"Clustering is a specialized discipline within Machine Learning aimed at separating your data into homogeneous groups with common characteristics. 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