mirror of
https://github.com/Brandon-Rozek/website.git
synced 2024-11-14 12:37:30 -05:00
121 lines
5.3 KiB
HTML
121 lines
5.3 KiB
HTML
|
<!DOCTYPE html>
|
||
|
|
<html>
|
||
|
|
<head>
|
||
|
|
<meta charset="utf-8" />
|
||
|
|
<meta name="author" content="Fredrik Danielsson, http://lostkeys.se">
|
||
|
|
<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>
|