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94 lines
3.3 KiB
HTML
94 lines
3.3 KiB
HTML
<!DOCTYPE html>
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<html>
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<head>
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<meta charset="utf-8" />
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<meta name="author" content="Brandon Rozek">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>Brandon Rozek</title>
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</head>
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<body>
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<aside class="main-nav">
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<nav>
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<ul>
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<a href="index.html%3Findex.html" data-shortcut="">
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Home
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Courses
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Lab Aide
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Presentations
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Research
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Transcript
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<main class="main-content">
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<article class="article">
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<h1>K-Medians</h1>
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<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>
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<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>
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<h3>Algorithm</h3>
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<p>Given an initial set of $k$ medians, the algorithm proceeds by alternating between two steps.</p>
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<p><strong>Assignment step</strong>: Assign each observation to the cluster whose median has the leas Manhattan distance.</p>
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<ul>
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<li>Intuitively this is finding the nearest median</li>
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</ul>
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<p><strong>Update Step</strong>: Calculate the new medians to be the centroids of the observations in the new clusters</p>
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<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>
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<p>The result depends on the initial clusters. It is common to run this multiple times with different starting conditions.</p>
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