{"id":337,"date":"2020-03-09T15:21:00","date_gmt":"2020-03-09T15:21:00","guid":{"rendered":"http:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/?p=337"},"modified":"2021-02-05T09:20:51","modified_gmt":"2021-02-05T09:20:51","slug":"stor-i-masterclass-professor-brendan-murphy","status":"publish","type":"post","link":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/2020\/03\/09\/stor-i-masterclass-professor-brendan-murphy\/","title":{"rendered":"STOR-i Masterclass: Professor Brendan Murphy"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"337\" class=\"elementor elementor-337\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-30464b7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"30464b7\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2ef2063\" data-id=\"2ef2063\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e15841f elementor-widget elementor-widget-heading\" data-id=\"e15841f\" 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\">Model-Based Clustering and Classification<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d440ce9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d440ce9\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4a693b1\" data-id=\"4a693b1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8f961e2 elementor-widget elementor-widget-text-editor\" data-id=\"8f961e2\" 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>A few weeks ago,\u00a0<a href=\"https:\/\/people.ucd.ie\/brendan.murphy\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"Professor Brendan Murphy (opens in a new tab)\">Professor Brendan Murphy<\/a>\u00a0visited 好色先生TV to present a two-day masterclass to all STOR-i students on Model-Based Clustering and Classification. Brendan is Full Professor and Head of School in School of Mathematics and Statistics at University College Dublin. His research interests include clustering, classification and latent variable modelling, particularly Brendan is interested in applications from social sciences, food science, medicine and biology. Currently, he is the editor for Social Sciences and Government for the Annals of Applied Statistics and he has recently co-authored a research monograph on Model-Based Clustering and Classification<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-891dacc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"891dacc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ef2a33e\" data-id=\"ef2a33e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3c1076b elementor-widget elementor-widget-heading\" data-id=\"3c1076b\" 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\">Intro<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a88e34a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a88e34a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6ed66ae\" data-id=\"6ed66ae\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2264ad3 elementor-widget elementor-widget-text-editor\" data-id=\"2264ad3\" 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><span style=\"font-size: 1.125rem\">Brendan kick-started the masterclass by providing an introduction to clustering. Cluster analysis aims to find meaningful groups in data in order to find clusters whose members have something in common that they do not share with members of other groups.\u00a0<\/span>Clustering dates back to the beginning of language &#8211; at least &#8211; when objects were grouped according to common characteristics. For example, Aristotle classified animals into groups based on observations, in <em>&#8216;History of Animals&#8217;<\/em> from the 4th century BC.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-76c66e9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"76c66e9\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-86ad67e\" data-id=\"86ad67e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3c6d239 elementor-widget elementor-widget-heading\" data-id=\"3c6d239\" 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\">Hierarchical Clustering<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bc384ce elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bc384ce\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3c9ce4c\" data-id=\"3c9ce4c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-05c3010 elementor-widget elementor-widget-text-editor\" data-id=\"05c3010\" 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>In the 1950s, various hierarchical clustering methods were introduced. These aim to build a tree of clusters so that you start with <em>n<\/em> observations divided into<em> n<\/em> clusters (every observation is its own, individual cluster), then you find the two<em> &#8216;closest&#8217;<\/em> clusters and group them so that there are now <em>n-1<\/em> clusters, then you continue in this way until everyone is in a cluster. In order to do this, you need a measure of distance between observations (dissimilarity) and a measure of distance between clusters (linkage). The choice of these measures can heavily influence the results. Hierarchical clustering doesn&#8217;t always perform well even though it is commonly used.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-08e0596 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"08e0596\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a61d572\" data-id=\"a61d572\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6c1b018 elementor-widget elementor-widget-image\" data-id=\"6c1b018\" 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 fetchpriority=\"high\" decoding=\"async\" width=\"540\" height=\"193\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/hierachy.png\" class=\"attachment-large size-large wp-image-340\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/hierachy.png 540w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/hierachy-300x107.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d75e080 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d75e080\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d13bbac\" data-id=\"d13bbac\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2c8fee5 elementor-widget elementor-widget-heading\" data-id=\"2c8fee5\" 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\">K-means Clustering<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-230464f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"230464f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b53490b\" data-id=\"b53490b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-65b30fe elementor-widget elementor-widget-text-editor\" data-id=\"65b30fe\" 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>Another method of clustering was developed in the late 1950s: k-means clustering. Here, we describe clusters by the average of the observations within it. This is an iterative algorithm repeated until convergence, split into two steps:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b5d01ad elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b5d01ad\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cc5e02b\" data-id=\"cc5e02b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-659e5c3 elementor-widget elementor-widget-text-editor\" data-id=\"659e5c3\" 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<ul><li>Allocation: assign observations to the cluster that is closest\u00a0<\/li><li>Update: the cluster summaries (i.e. the mean)<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1ee6b7f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1ee6b7f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e5fdfaf\" data-id=\"e5fdfaf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-27c739b elementor-widget elementor-widget-text-editor\" data-id=\"27c739b\" 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>Brendan demonstrated k-means clustering in action, by clustering the colours on pixals in an image on Alexandra Square, 好色先生TV. We start with a single cluster (k=1) and the results look pretty grey, as the number of clusters increases the photograph becomes more identifiable. Even with 2 clusters, buildings, shadows and people are all visible since light and dark areas have been separated. By the time we hit 10 clusters, the image is starting to look similar to the original and for 100 clusters, the image is indistinguishable from the original.&nbsp;<br><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7ecdb1d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7ecdb1d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-284a4b9\" data-id=\"284a4b9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-eb19ee4 elementor-widget elementor-widget-image\" data-id=\"eb19ee4\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"658\" height=\"439\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq1-1.png\" class=\"attachment-large size-large wp-image-343\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq1-1.png 658w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq1-1-300x200.png 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">k=1<\/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-33 elementor-top-column elementor-element elementor-element-afd20bf\" data-id=\"afd20bf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f3f0d23 elementor-widget elementor-widget-image\" data-id=\"f3f0d23\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"661\" height=\"441\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq2.png\" class=\"attachment-large size-large wp-image-344\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq2.png 661w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq2-300x200.png 300w\" sizes=\"(max-width: 661px) 100vw, 661px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">k=2<\/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-33 elementor-top-column elementor-element elementor-element-645311c\" data-id=\"645311c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a108ae9 elementor-widget elementor-widget-image\" data-id=\"a108ae9\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"660\" height=\"443\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq3.png\" class=\"attachment-large size-large wp-image-345\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq3.png 660w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq3-300x201.png 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">k=3<\/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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-43777b8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"43777b8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-1dbe79a\" data-id=\"1dbe79a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-325f5f6 elementor-widget elementor-widget-image\" data-id=\"325f5f6\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"659\" height=\"441\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq4.png\" class=\"attachment-large size-large wp-image-346\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq4.png 659w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq4-300x201.png 300w\" sizes=\"(max-width: 659px) 100vw, 659px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">k=10<\/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-33 elementor-top-column elementor-element elementor-element-6903a06\" data-id=\"6903a06\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-40fcbba elementor-widget elementor-widget-image\" data-id=\"40fcbba\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"660\" height=\"442\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq5.png\" class=\"attachment-large size-large wp-image-347\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq5.png 660w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq5-300x201.png 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">k=20<\/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-33 elementor-top-column elementor-element elementor-element-e8ffad3\" data-id=\"e8ffad3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fdc845c elementor-widget elementor-widget-image\" data-id=\"fdc845c\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"658\" height=\"442\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq6.png\" class=\"attachment-large size-large wp-image-348\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq6.png 658w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/Alexsq6-300x202.png 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">k=100<\/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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ab25bca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ab25bca\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-92b4ee2\" data-id=\"92b4ee2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6d90e0a elementor-widget elementor-widget-heading\" data-id=\"6d90e0a\" 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\">Model-Based Clustering<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-46a1f1c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"46a1f1c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cbff5c3\" data-id=\"cbff5c3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aa7e7a2 elementor-widget elementor-widget-text-editor\" data-id=\"aa7e7a2\" 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 first successful model-based clustering method was also developed in the 1950s by Paul Lazarsfeld for multi-variate discrete data. The model he proposed is now known as the Latent Class Model &#8211; he used the term &#8216;latent&#8217; for unknown cluster allocations.&nbsp;<\/p>\n<p>The dominant model for model-based clustering of continuous data was developed in 1963 by John Wolfe, this is known as the Gaussian Mixture Model.&nbsp;<\/p>\n<p>Model-based clustering assumes that observations arise from a finite mixture model and that each observation has a probability that it came from each group, g &#8211; these probabilities are called the mixing proportions. The data within each group is modelled and we can combine this model, with the mixing proportions, to define an overall model for the data. Many modes of estimating these models are available, Brendan focussed on the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Expectation%E2%80%93maximization_algorithm\">EM algorithm<\/a>.&nbsp;<\/p>\n<p>A Gaussian mixture model models each observation as a multivariate Gaussian distribution. Therefore the clusters correspond to Gaussian densities and have elliptical shapes. We use the EM algorithm to fit these Gaussian mixture models. The example below fit these clusters in just 7 iterations of the algorithm.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8e21a92 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8e21a92\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-9b68f84\" data-id=\"9b68f84\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3b38ffd elementor-widget elementor-widget-image\" data-id=\"3b38ffd\" 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=\"688\" height=\"548\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/cluster1.png\" class=\"attachment-large size-large wp-image-349\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/cluster1.png 867w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/cluster1-300x239.png 300w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/cluster1-768x611.png 768w\" sizes=\"(max-width: 688px) 100vw, 688px\" \/>\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<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-4b249eb\" data-id=\"4b249eb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-42f1286 elementor-widget elementor-widget-image\" data-id=\"42f1286\" 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=\"688\" height=\"577\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/cluster2.png\" class=\"attachment-large size-large wp-image-350\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/cluster2.png 846w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/cluster2-300x251.png 300w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/cluster2-768x644.png 768w\" sizes=\"(max-width: 688px) 100vw, 688px\" \/>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-166076c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"166076c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0068a43\" data-id=\"0068a43\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-901ff70 elementor-widget elementor-widget-heading\" data-id=\"901ff70\" 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\">Further Reading <\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d94e875 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d94e875\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-60201be\" data-id=\"60201be\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-da3f1ec elementor-widget elementor-widget-text-editor\" data-id=\"da3f1ec\" 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>Brendan recommended some further reading:<\/p>\n<ul>\n<li>Geoffrey McLachlan and Kaye Basford<br \/><i>Mixture Models: Inference and Applications to Clustering<\/i><\/li>\n<li>Collins, Linda M and Stephanie Lanza<br \/><i>Latent Class and Latent Transition Analysis<\/i><\/li>\n<li>Paul McNicholas<br \/><i>Mixture Model-Based Classification<\/i><\/li>\n<li>Charles Bouveyron, Gilles Celeux, Brendan Murphy and Adrian Raftery<br \/><i>Model-Based Clustering and Classification for Data Science\u00a0<\/i><\/li>\n<\/ul>\n<div><span style=\"font-family: Raleway, sans-serif\"><span style=\"font-size: 18px\">Brendan is an author for the &#8216;<b>mclust<\/b>&#8216; package in R. This is used for model-based clustering, classification and density estimation based on finite Gaussian mixture-modelling fitted via the EM algorithm. This package had 1.5 million downloads in 2019!<\/span><\/span><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ea0d136 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ea0d136\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-71e7444\" data-id=\"71e7444\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a65f8a0 elementor-widget elementor-widget-image\" data-id=\"a65f8a0\" 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=\"498\" height=\"225\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-content\/uploads\/sites\/6\/2020\/02\/giphy.gif\" class=\"attachment-large size-large wp-image-368\" 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\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fa4ae7c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fa4ae7c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c8c96f0\" data-id=\"c8c96f0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-67052ea elementor-widget elementor-widget-text-editor\" data-id=\"67052ea\" 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>This masterclass was my first and I really enjoyed learning about clustering and classification with Professor Brendan Murphy. I found the history, methods and applications really interesting and I am looking forward to reading further into the topic.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Model-Based Clustering and Classification A few weeks ago,&nbsp;Professor Brendan Murphy&nbsp;visited 好色先生TV to present a two-day masterclass to all STOR-i&hellip;<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[9,4],"class_list":["post-337","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-clustering","tag-stor-i"],"_links":{"self":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/posts\/337","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/comments?post=337"}],"version-history":[{"count":25,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/posts\/337\/revisions"}],"predecessor-version":[{"id":378,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/posts\/337\/revisions\/378"}],"wp:attachment":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/media?parent=337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/categories?post=337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/eleanor-darcy\/wp-json\/wp\/v2\/tags?post=337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}