<!DOCTYPE html> <html> <head> <meta charset="utf-8" /> <meta name="author" content="Brandon Rozek"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <meta name="robots" content="noindex" /> <title>Brandon Rozek</title> <link rel="stylesheet" href="themes/bitsandpieces/styles/main.css" type="text/css" /> <link rel="stylesheet" href="themes/bitsandpieces/styles/highlightjs-github.css" type="text/css" /> </head> <body> <aside class="main-nav"> <nav> <ul> <li class="menuitem "> <a href="index.html%3Findex.html" data-shortcut=""> Home </a> </li> <li class="menuitem "> <a href="index.html%3Fcourses.html" data-shortcut=""> Courses </a> </li> <li class="menuitem "> <a href="index.html%3Flabaide.html" data-shortcut=""> Lab Aide </a> </li> <li class="menuitem "> <a href="index.html%3Fpresentations.html" data-shortcut=""> Presentations </a> </li> <li class="menuitem "> <a href="index.html%3Fresearch.html" data-shortcut=""> Research </a> </li> <li class="menuitem "> <a href="index.html%3Ftranscript.html" data-shortcut=""> Transcript </a> </li> </ul> </nav> </aside> <main class="main-content"> <article class="article"> <h1>Divisive Methods Pt 2.</h1> <p>Recall in the previous section that we spoke about Monothetic and Polythetic methods. Monothetic methods only looks at a single variable at a time while Polythetic looks at multiple variables simultaneously. In this section, we will speak more about polythetic divisive methods.</p> <h2>Polythetic Divisive Methods</h2> <p>Polythetic methods operate via a distance matrix.</p> <p>This procedure avoids considering all possible splits by </p> <ol> <li>Finding the object that is furthest away from the others within a group and using that as a seed for a splinter group.</li> <li>Each object is then considered for entry to that separate splinter group: any that are closer to the splinter group than the main group is moved to the splinter one. </li> <li>The step is then repeated.</li> </ol> <p>This process has been developed into a program named <code>DIANA</code> (DIvisive ANAlysis Clustering) which is implemented in <code>R</code>.</p> <h3>Similarities to Politics</h3> <p>This somewhat resembles a way a political party might split due to inner conflicts.</p> <p>Firstly, the most discontented member leaves the party and starts a new one, and then some others follow him until a kind of equilibrium is attained.</p> <h2>Methods for Large Data Sets</h2> <p>There are two common hierarchical methods used for large data sets <code>BIRCH</code> and <code>CURE</code>. Both of these algorithms employ a pre-clustering phase in where dense regions are summarized, the summaries being then clustered using a hierarchical method based on centroids.</p> <h3>CURE</h3> <ol> <li><code>CURE</code> starts with a random sample of points and represents clusters by a smaller number of points that capture the shape of the cluster</li> <li>Which are then shrunk towards the centroid as to dampen the effect of the outliers</li> <li>Hierarchical clustering then operates on the representative points</li> </ol> <p><code>CURE</code> has been shown to be able to cope with arbitrary-shaped clusters and in that respect may be superior to <code>BIRCH</code>, although it does require judgment as to the number of clusters and also a parameter which favors either more or less compact clusters.</p> <h2>Revisiting Topics: Cluster Dissimilarity</h2> <p>In order to decide where clusters should be combined (for agglomerative), or where a cluster should be split (for divisive), a measure of dissimilarity between sets of observations is required.</p> <p>In most methods of hierarchical clustering this is achieved by a use of an appropriate </p> <ul> <li>Metric (a measure of distance between pairs of observations)</li> <li>Linkage Criterion (which specifies the dissimilarities of sets as functions of pairwise distances observations in the sets)</li> </ul> <h2>Advantages of Hierarchical Clustering</h2> <ul> <li>Any valid measure of distance measure can be used</li> <li>In most cases, the observations themselves are not required, just hte matrix of distances <ul> <li>This can have the advantage of only having to store a distance matrix in memory as opposed to a n-dimensional matrix.</li> </ul></li> </ul> </article> </main> <script src="themes/bitsandpieces/scripts/highlight.js"></script> <script src="themes/bitsandpieces/scripts/mousetrap.min.js"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: { inlineMath: [ ['$','$'], ["\\(","\\)"] ], processEscapes: true } }); </script> <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"> </script> <script> hljs.initHighlightingOnLoad(); document.querySelectorAll('.menuitem a').forEach(function(el) { if (el.getAttribute('data-shortcut').length > 0) { Mousetrap.bind(el.getAttribute('data-shortcut'), function() { location.assign(el.getAttribute('href')); }); } }); </script> </body> </html>