{"id":170459,"date":"2023-09-10T15:12:55","date_gmt":"2023-09-10T14:12:55","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=170459"},"modified":"2023-10-30T20:01:11","modified_gmt":"2023-10-30T19:01:11","slug":"exploring-the-agglomerative-hierarchical-custering-algorithm-ahc","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/exploring-the-agglomerative-hierarchical-custering-algorithm-ahc","title":{"rendered":"Exploring the Agglomerative Hierarchical Custering algorithm (AHC)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"170459\" class=\"elementor elementor-170459\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-23630a1 e-flex e-con-boxed e-con\" data-id=\"23630a1\" 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<div class=\"elementor-element elementor-element-762332b e-con-full e-flex e-con\" data-id=\"762332b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-134ff24 elementor-widget elementor-widget-heading\" data-id=\"134ff24\" 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\">Hierarchical Clustering\u00a0 Algorithm(AHC): Clustering is a specific discipline within Machine Learning with the goal of dividing your data into homogeneous groups with common characteristics. This is a highly valued field, especially in marketing, where the aim is often to segment customer databases to identify specific behaviors.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fd68469 elementor-widget elementor-widget-text-editor\" data-id=\"fd68469\" 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 a previous article, we introduced a clustering algorithm known as K-means.<\/p><p>In this article, we will delve into the workings of the Agglomerative Hierarchical Clustering\u00a0 Algorithm(AHC). The <strong>Agglomerative Hierarchical Clustering Algorithm(AHC)<\/strong> is a well-known unsupervised algorithm in the field of clustering.<\/p><p>Its applications are diverse, including customer segmentation, <a href=\"https:\/\/datascientest.com\/en\/data-analysis-course-face-to-face-or-online-whats-the-best-choice\">data analysis<\/a>, image segmentation, and semi-supervised learning, among others.<\/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-c6f9024 elementor-widget elementor-widget-heading\" data-id=\"c6f9024\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Hierarchical Clustering\u00a0 Algorithm(AHC) - The Principle <\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0bbb20e elementor-widget elementor-widget-text-editor\" data-id=\"0bbb20e\" 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>Given points and an integer k, <a href=\"https:\/\/datascientest.com\/en\/algorithm-what-is-it\">the 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:<\/p>\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-f1f1701 e-flex e-con-boxed e-con\" data-id=\"f1f1701\" 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<div class=\"elementor-element elementor-element-b0eb990 e-con-full e-flex e-con\" data-id=\"b0eb990\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c859ab7 elementor-widget elementor-widget-image\" data-id=\"c859ab7\" 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=\"383\" height=\"374\" src=\"https:\/\/datascientest.com\/en\/files\/2020\/06\/unnamed-4.png\" class=\"attachment-large size-large wp-image-3696\" alt=\"clusters\" srcset=\"https:\/\/datascientest.com\/en\/files\/2020\/06\/unnamed-4.png 383w, https:\/\/datascientest.com\/en\/files\/2020\/06\/unnamed-4-300x293.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/>\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<\/div>\n\t\t<div class=\"elementor-element elementor-element-9d03e4f e-con-full e-flex e-con\" data-id=\"9d03e4f\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0d95bc1 elementor-widget elementor-widget-image\" data-id=\"0d95bc1\" 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=\"379\" height=\"383\" src=\"https:\/\/datascientest.com\/en\/files\/2020\/06\/unnamed-5.png\" class=\"attachment-large size-large wp-image-3697\" alt=\"clusters\" srcset=\"https:\/\/datascientest.com\/en\/files\/2020\/06\/unnamed-5.png 379w, https:\/\/datascientest.com\/en\/files\/2020\/06\/unnamed-5-297x300.png 297w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/>\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<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8f5ce01 e-flex e-con-boxed e-con\" data-id=\"8f5ce01\" 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<div class=\"elementor-element elementor-element-c21a39c e-con-full e-flex e-con\" data-id=\"c21a39c\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ab1d6d8 elementor-widget elementor-widget-text-editor\" data-id=\"ab1d6d8\" 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>On this 2D dataset, it&#8217;s clear that we can divide it into 3 groups. How do we go about it concretely?<\/p><p>The initial idea is to consider that each point in your dataset is a centroid. This means that each point corresponds to a unique label (0, 1, 2, 3, 4&#8230;). <br \/>Then, we group each centroid with its nearest neighbor centroid. The latter takes on the label of the centroid that &#8220;absorbed&#8221; it. <br \/>Next, we calculate the new centroids, which will be the centers of gravity of the newly created clusters. <br \/>We repeat this process until we obtain a single cluster or a predefined number of clusters.<\/p><p>In our example, the optimal number of clusters is 3, and the final result is shown on the right-hand side.<\/p>\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-6f4ca4e e-flex e-con-boxed e-con\" data-id=\"6f4ca4e\" 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<div class=\"elementor-element elementor-element-d860a53 e-con-full e-flex e-con\" data-id=\"d860a53\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ab818a4 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"ab818a4\" 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\">Data Science 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<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-e248534 e-flex e-con-boxed e-con\" data-id=\"e248534\" 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<div class=\"elementor-element elementor-element-5db37a4b e-con-full e-flex e-con\" data-id=\"5db37a4b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-54d036d4 elementor-widget elementor-widget-text-editor\" data-id=\"54d036d4\" 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: 400;\">To better understand the mechanism of the Hierarchical Clustering\u00a0 Algorithm(AHC), we can illustrate it with a simple diagram:<\/span><\/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-54cb003f elementor-widget elementor-widget-image\" data-id=\"54cb003f\" 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=\"404\" height=\"336\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/Capture-decran-2020-06-12-a-16.12.42.png\" class=\"attachment-large size-large wp-image-170464\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/Capture-decran-2020-06-12-a-16.12.42.png 404w, https:\/\/datascientest.com\/en\/files\/2023\/09\/Capture-decran-2020-06-12-a-16.12.42-300x250.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/>\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<div class=\"elementor-element elementor-element-2f847576 elementor-widget elementor-widget-text-editor\" data-id=\"2f847576\" 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: 400;\">At the beginning, each letter is considered as a cluster, and then they are gradually grouped together based on their proximity to eventually form only one group: abcdef.<\/span><\/p>\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-fbd1f01 e-flex e-con-boxed e-con\" data-id=\"fbd1f01\" 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<div class=\"elementor-element elementor-element-56a4a572 e-con-full e-flex e-con\" data-id=\"56a4a572\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5d892e78 elementor-widget elementor-widget-heading\" data-id=\"5d892e78\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Hierarchical Clustering\u00a0 Algorithm(AHC): Distance criteria<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-134280fa elementor-widget elementor-widget-text-editor\" data-id=\"134280fa\" 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 will understand that in the Hierarchical Clustering\u00a0 Algorithm(AHC), three key points are:<\/p><p>1. What metric is used to evaluate the distance between centroids?<br \/>2. How many clusters should be chosen?<br \/>3. On what criterion do we decide to group centroids together?<\/p><p>In <strong>hierarchical agglomerative clustering,<\/strong> the distance typically used is the Euclidean distance, 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<div class=\"elementor-element elementor-element-1a7feba9 elementor-widget elementor-widget-image\" data-id=\"1a7feba9\" 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=\"79\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/distance-euclidienne.png\" class=\"attachment-large size-large wp-image-170465\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/distance-euclidienne.png 833w, https:\/\/datascientest.com\/en\/files\/2023\/09\/distance-euclidienne-300x30.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/09\/distance-euclidienne-768x76.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<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-adf83dc e-flex e-con-boxed e-con\" data-id=\"adf83dc\" 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<div class=\"elementor-element elementor-element-65cd065 e-con-full e-flex e-con\" data-id=\"65cd065\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c022a84 elementor-widget elementor-widget-text-editor\" data-id=\"c022a84\" 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 us to evaluate the distance between centroids. At each step of merging two centroids, a new cluster is formed, and a new centroid is calculated, which is simply the center of gravity of the data points within that cluster, as explained earlier.<\/p><p>This is where the concept of intra-cluster inertia comes into play. It&#8217;s simply the sum of the <strong>Euclidean distances<\/strong> between each point associated with the cluster and the newly calculated center of gravity. Naturally, when you merge clusters, you increase the intra-cluster inertia. The challenge is to minimize this increase. Thus, if you have the choice of merging a cluster with 4 or 5 other different clusters, you would choose the one that minimizes the increase in intra-cluster inertia.<\/p><p>This method is the principle of Ward&#8217;s criterion, which is often used for Hierarchical Agglomerative Clustering. There are other criteria, but <strong>Ward&#8217;s criterion<\/strong> is the default when implementing hierarchical agglomerative <a href=\"https:\/\/datascientest.com\/en\/python-programming-for-beginners-episode-3\">clustering in Python with Scikit Learn.<\/a><\/p><p>In the previous example, it was easy to find the ideal number of clusters by visually inspecting the data. However, datasets often have more than two dimensions, making it difficult to visualize the data and quickly identify the optimal number of clusters. You can decide the number of clusters beforehand when using the <strong>Hierarchical Clustering\u00a0 Algorithm(AHC)<\/strong>. Suppose in the previous example we hadn&#8217;t visualized the data beforehand and decided to test with different 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<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1fa6056 e-flex e-con-boxed e-con\" data-id=\"1fa6056\" 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<div class=\"elementor-element elementor-element-7b13452d e-con-full e-flex e-con\" data-id=\"7b13452d\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2c1869f6 elementor-widget elementor-widget-image\" data-id=\"2c1869f6\" 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=\"512\" height=\"140\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/unnamed-6.png\" class=\"attachment-large size-large wp-image-170466\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/unnamed-6.png 512w, https:\/\/datascientest.com\/en\/files\/2023\/09\/unnamed-6-300x82.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/>\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<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9901412 e-flex e-con-boxed e-con\" data-id=\"9901412\" 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<div class=\"elementor-element elementor-element-ef282ca e-con-full e-flex e-con\" data-id=\"ef282ca\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d5c3271 elementor-widget elementor-widget-text-editor\" data-id=\"d5c3271\" 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 incorrect because the optimal number of clusters is 3. A well-known method for finding the optimal number of clusters is to use a dendrogram like this one:<\/p>\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-c1b2f7f e-flex e-con-boxed e-con\" data-id=\"c1b2f7f\" 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<div class=\"elementor-element elementor-element-c3fb005 e-con-full e-flex e-con\" data-id=\"c3fb005\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-70b2918b elementor-widget elementor-widget-image\" data-id=\"70b2918b\" 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=\"512\" height=\"413\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/unnamed-7.png\" class=\"attachment-large size-large wp-image-170467\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/09\/unnamed-7.png 512w, https:\/\/datascientest.com\/en\/files\/2023\/09\/unnamed-7-300x242.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/>\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<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-625cb81 e-flex e-con-boxed e-con\" data-id=\"625cb81\" 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<div class=\"elementor-element elementor-element-53e524a e-con-full e-flex e-con\" data-id=\"53e524a\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e4cfe24 elementor-widget elementor-widget-text-editor\" data-id=\"e4cfe24\" 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 visualize the successive groupings until you get a single cluster. It is often relevant to choose the partition corresponding to the largest jump between two consecutive clusters.<\/p><p>The number of clusters then corresponds to the number of vertical lines crossed by the horizontal cut of the dendrogram. In our example above, the horizontal cut corresponds to the two red lines. There are 3 vertical lines crossed by the cut. We can deduce that the optimal number of clusters is 3.<\/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-2297bb5 elementor-widget elementor-widget-heading\" data-id=\"2297bb5\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Let's get practical with Python and Hierarchical Clustering\u00a0 Algorithm (AHC)<\/h2>\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-c9d0c9f e-flex e-con-boxed e-con\" data-id=\"c9d0c9f\" 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<div class=\"elementor-element elementor-element-a4e1a8e e-con-full e-flex e-con\" data-id=\"a4e1a8e\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e9ae42b elementor-widget elementor-widget-text-editor\" data-id=\"e9ae42b\" 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 training of a <strong>Hierarchical Clustering\u00a0 Algorithm(AHC)<\/strong> is facilitated with the <strong>Scikit-Learn library<\/strong>. A dataset like the one used in the example can be easily created using Scikit-Learn&#8217;s make_blobs functionality.<\/p><p>Once our dataset is generated, we can proceed with the implementation of AHC. We will use the Scikit-Learn library.<\/p><p>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<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c87f77b e-flex e-con-boxed e-con\" data-id=\"c87f77b\" 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<div class=\"elementor-element elementor-element-09cf1c6 e-con-full e-flex e-con\" data-id=\"09cf1c6\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-02737c1 elementor-widget elementor-widget-shortcode\" data-id=\"02737c1\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\"https:\/\/gist.github.com\/Thibault-venet\/3f7bd86a28508b8fed42aef1772d8ece.js\"><\/script><\/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-41071e4 e-con-full e-flex e-con\" data-id=\"41071e4\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-87e6ecb elementor-align-center elementor-widget elementor-widget-button\" data-id=\"87e6ecb\" 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\">Learn to code in Python<\/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<\/div>\n\t\t<div class=\"elementor-element elementor-element-56043b8 e-flex e-con-boxed e-con\" data-id=\"56043b8\" 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<div class=\"elementor-element elementor-element-6d383c6 e-con-full e-flex e-con\" data-id=\"6d383c6\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b66a7fc elementor-widget elementor-widget-text-editor\" data-id=\"b66a7fc\" 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 allows you to specify the number of clusters desired for the classification. By default, the distance used is the Euclidean distance. Also, the &#8220;linkage criterion&#8221; called linkage is set to the Ward criterion by default.<\/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-83c7e47 elementor-widget elementor-widget-heading\" data-id=\"83c7e47\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Hierarchical Clustering\u00a0Algorithm(AHC): The limits<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ebe57f1 elementor-widget elementor-widget-text-editor\" data-id=\"ebe57f1\" 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>As we have seen, the algorithm requires defining the number of partitions beforehand. This demands a precise idea, and even though we have seen a method to optimize for some datasets, it is not foolproof. For instance, datasets with elliptical shapes may pose a problem.<\/p><p>In the example below, it&#8217;s evident that there are two groups resembling two ellipses. The figure on the right shows the result after using<strong> AHC,<\/strong> and it&#8217;s clear that it didn&#8217;t manage to identify our two ellipses.<\/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-2699e40 elementor-widget elementor-widget-image\" data-id=\"2699e40\" 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=\"512\" height=\"220\" src=\"https:\/\/datascientest.com\/en\/files\/2020\/06\/CAH4.png\" class=\"attachment-large size-large wp-image-3692\" alt=\"CAH\" srcset=\"https:\/\/datascientest.com\/en\/files\/2020\/06\/CAH4.png 512w, https:\/\/datascientest.com\/en\/files\/2020\/06\/CAH4-300x129.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/>\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<div class=\"elementor-element elementor-element-ca0422d elementor-widget elementor-widget-text-editor\" data-id=\"ca0422d\" 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>Also, hierarchical agglomerative clustering can quickly become very time and resource-consuming. One way to circumvent this problem is by providing a connectivity matrix. This is a sparse matrix indicating which pairs of observations are neighbors.<\/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-a4ca433 elementor-widget elementor-widget-text-editor\" data-id=\"a4ca433\" 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>Using a clustering algorithm like <strong>Hierarchical Agglomerative Clustering<\/strong> is not always straightforward depending on the data you have. You often need to preprocess the data. At DataScientest, we teach you how to master the main clustering algorithms and interpret them on various datasets. Don&#8217;t hesitate to explore our training offers to learn how to master clustering algorithms and many other areas of Machine Learning.<\/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-5d5cd0f elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"5d5cd0f\" 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-sm elementor-animation-grow\" 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\">Data Science 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<\/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>Hierarchical Clustering&nbsp; Algorithm(AHC): Clustering is a specific discipline within Machine Learning with the goal of dividing your data into homogeneous groups with common characteristics. This is a highly valued field, especially in marketing, where the aim is often to segment customer databases to identify specific behaviors. In a previous article, we introduced a clustering algorithm [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":170460,"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>Exploring the Agglomerative Hierarchical Custering algorithm (AHC)<\/title>\n<meta name=\"description\" content=\"Agglomerative Hierarchical Custering algorithm (AHC): If you want to know about the Agglomerative Hierarchical Custering algorithm (AHC),\" \/>\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\/exploring-the-agglomerative-hierarchical-custering-algorithm-ahc\" 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