mirror of
https://github.com/Brandon-Rozek/website.git
synced 2024-11-29 23:52:21 -05:00
101 lines
4.5 KiB
HTML
101 lines
4.5 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>Introduction to Connectivity Based Models</h1>
|
||
|
|
<p>Hierarchical algorithms combine observations to form clusters based on their distance.</p>
|
||
|
|
<h2>Connectivity Methods</h2>
|
||
|
|
<p>Hierarchal Clustering techniques can be subdivided depending on the method of going about it.</p>
|
||
|
|
<p>First there are two different methods in forming the clusters <em>Agglomerative</em> and <em>Divisive</em></p>
|
||
|
|
<p><u>Agglomerative</u> is when you combine the n individuals into groups through each iteration</p>
|
||
|
|
<p><u>Divisive</u> is when you are separating one giant group into finer groupings with each iteration.</p>
|
||
|
|
<p>Hierarchical methods are an irrevocable algorithm, once it joins or separates a grouping, it cannot be undone. As Kaufman and Rousseeuw (1990) colorfully comment: <em>"A hierarchical method suffers from the defect that it can never repair what was done in previous steps"</em>. </p>
|
||
|
|
<p>It is the job of the statistician to decide when to stop the agglomerative or decisive algorithm, since having one giant cluster containing all observations or having each observation be a cluster isn't particularly useful.</p>
|
||
|
|
<p>At different distances, different clusters are formed and are more readily represented using a <strong>dendrogram</strong>. These algorithms do not provide a unique solution but rather provide an extensive hierarchy of clusters that merge or divide at different distances.</p>
|
||
|
|
<h2>Linkage Criterion</h2>
|
||
|
|
<p>Apart from the method of forming clusters, the user also needs to decide on a linkage criterion to use. Meaning, how do you want to optimize your clusters.</p>
|
||
|
|
<p>Do you want to group based on the nearest points in each cluster? Nearest Neighbor Clustering</p>
|
||
|
|
<p>Or do you want to based on the farthest observations in each cluster? Farthest neighbor clustering.</p>
|
||
|
|
<p><img src="http://www.multid.se/genex/onlinehelp/clustering_distances.png" alt="http://www.multid.se/genex/onlinehelp/clustering_distances.png" /></p>
|
||
|
|
<h2>Shortcomings</h2>
|
||
|
|
<p>This method is not very robust towards outliers, which will either show up as additional clusters or even cause other clusters to merge depending on the clustering method.</p>
|
||
|
|
<p>As we go through this section, we will go into detail about the different linkage criterion and other parameters of this model.</p>
|
||
|
|
</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>
|