mirror of
https://github.com/Brandon-Rozek/website.git
synced 2024-12-23 16:31:10 +00:00
118 lines
4.6 KiB
HTML
118 lines
4.6 KiB
HTML
<!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>K-Medoids</h1>
|
|
<p>A medoid can be defined as the object of a cluster whose average dissimilarity to all the objects in the cluster is minimal.</p>
|
|
<p>The K-medoids algorithm is related to k-means and the medoidshift algorithm. Both the k-means and k-medoids algorithms are partition and both attempt to minimize the distance between points in the cluster to it's center. In contrast to k-means, it chooses data points as centers and uses the Manhattan Norm to define the distance between data points instead of the Euclidean.</p>
|
|
<p>This method is known to be more robust to noise and outliers compared to k-means since it minimizes the sum of pairwise dissimilarities instead of the sum of squared Euclidean distances.</p>
|
|
<h2>Algorithms</h2>
|
|
<p>There are several algorithms that have been created as an optimization to an exhaustive search. In this section, we'll discuss PAM and Voronoi iteration method.</p>
|
|
<h3>Partitioning Around Medoids (PAM)</h3>
|
|
<ol>
|
|
<li>Select $k$ of the $n$ data points as medoids</li>
|
|
<li>Associate each data point to the closes medoid</li>
|
|
<li>While the cost of the configuration decreases:
|
|
<ol>
|
|
<li>For each medoid $m$, for each non-medoid data point $o$:
|
|
<ol>
|
|
<li>Swap $m$ and $o$, recompute the cost (sum of distances of points to their medoid)</li>
|
|
<li>If the total cost of the configuration increased in the previous step, undo the swap</li>
|
|
</ol></li>
|
|
</ol></li>
|
|
</ol>
|
|
<h3>Voronoi Iteration Method</h3>
|
|
<ol>
|
|
<li>Select $k$ of the $n$ data points as medoids</li>
|
|
<li>While the cost of the configuration decreases
|
|
<ol>
|
|
<li>In each cluster, make the point that minimizes the sum of distances within the cluster the medoid</li>
|
|
<li>Reassign each point to the cluster defined by the closest medoid determined in the previous step.</li>
|
|
</ol></li>
|
|
</ol>
|
|
<h3>Clustering Large Applications (CLARA</h3>
|
|
<p>This is a variant of the PAM algorithm that relies on the sampling approach to handle large datasets. The cost of a particular cluster configuration is the mean cost of all the dissimilarities.</p>
|
|
<h2>R Implementations</h2>
|
|
<p>Both PAM and CLARA are defined in the <code>cluster</code> package in R.</p>
|
|
<pre><code class="language-R">clara(x, k, metric = "euclidean", stand = FALSE, samples = 5,
|
|
sampsize = min(n, 40 + 2 * k), trace = 0, medoids.x = TRUE,
|
|
keep.data = medoids.x, rngR = FALSE)</code></pre>
|
|
<pre><code class="language-R">pam(x, k, metric = "euclidean", stand = FALSE)</code></pre>
|
|
</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>
|