mirror of
https://github.com/Brandon-Rozek/website.git
synced 2024-12-24 13:11:18 +00:00
94 lines
3.3 KiB
HTML
94 lines
3.3 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>K-Medians</h1>
|
|
<p>This is a variation of k-means clustering where instead of calculating the mean for each cluster to determine its centroid we are going to calculate the median instead.</p>
|
|
<p>This has the effect of minimizing error over all the clusters with respect to the Manhattan norm as opposed to the Euclidean squared norm which is minimized in K-means</p>
|
|
<h3>Algorithm</h3>
|
|
<p>Given an initial set of $k$ medians, the algorithm proceeds by alternating between two steps.</p>
|
|
<p><strong>Assignment step</strong>: Assign each observation to the cluster whose median has the leas Manhattan distance.</p>
|
|
<ul>
|
|
<li>Intuitively this is finding the nearest median</li>
|
|
</ul>
|
|
<p><strong>Update Step</strong>: Calculate the new medians to be the centroids of the observations in the new clusters</p>
|
|
<p>The algorithm is known to have converged when assignments no longer change. There is no guarantee that the optimum is found using this algorithm. </p>
|
|
<p>The result depends on the initial clusters. It is common to run this multiple times with different starting conditions.</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>
|