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97 lines
3.1 KiB
HTML
97 lines
3.1 KiB
HTML
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<!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="Fredrik Danielsson, http://lostkeys.se">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<meta name="robots" content="noindex" />
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<title>Brandon Rozek</title>
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<link rel="stylesheet" href="themes/bitsandpieces/styles/main.css" type="text/css" />
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<link rel="stylesheet" href="themes/bitsandpieces/styles/highlightjs-github.css" type="text/css" />
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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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<li class="menuitem ">
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<a href="index.html%3Findex.html" data-shortcut="">
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Home
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</a>
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</li>
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<li class="menuitem ">
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<a href="index.html%3Fcourses.html" data-shortcut="">
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Courses
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</a>
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</li>
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<li class="menuitem ">
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<a href="index.html%3Flabaide.html" data-shortcut="">
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Lab Aide
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</a>
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</li>
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<li class="menuitem ">
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<a href="index.html%3Fpresentations.html" data-shortcut="">
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Presentations
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</a>
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</li>
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<li class="menuitem ">
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<a href="index.html%3Fresearch.html" data-shortcut="">
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Research
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</a>
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</li>
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<li class="menuitem ">
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<a href="index.html%3Ftranscript.html" data-shortcut="">
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Transcript
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</a>
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</li>
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</ul>
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</nav>
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</aside>
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<main class="main-content">
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<article class="article">
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<h1>Revisiting Similarity Measures</h1>
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<h2>Manhatten Distance</h2>
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<p>An additional use case for Manhatten distance is when dealing with binary vectors. This approach, otherwise known as the Hamming distance, is the number of bits that are different between two binary vectors.</p>
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<h2>Ordinal Variables</h2>
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<p>Ordinal variables can be treated as if they were on a interval scale.</p>
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<p>First, replace the ordinal variable value by its rank ($r_{if}$) Then map the range of each variable onto the interval $[0, 1]$ by replacing the $f<em>i$ where f is the variable and i is the object by
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$$
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z</em>{if} = \frac{r_{if} - 1}{M_f - 1}
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$$
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Where $M_f$ is the maximum rank.</p>
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<h3>Example</h3>
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<p>Freshman = $0$ Sophmore = $\frac{1}{3}$ Junior = $\frac{2}{3}$ Senior = $1$</p>
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<p>$d(freshman, senior) = 1$</p>
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<p>$d(junior, senior) = \frac{1}{3}$</p>
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</article>
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</main>
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<script src="themes/bitsandpieces/scripts/highlight.js"></script>
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<script src="themes/bitsandpieces/scripts/mousetrap.min.js"></script>
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<script type="text/x-mathjax-config">
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MathJax.Hub.Config({
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tex2jax: {
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inlineMath: [ ['$','$'], ["\\(","\\)"] ],
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processEscapes: true
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}
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});
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</script>
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<script type="text/javascript"
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src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
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</script>
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<script>
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hljs.initHighlightingOnLoad();
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document.querySelectorAll('.menuitem a').forEach(function(el) {
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if (el.getAttribute('data-shortcut').length > 0) {
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Mousetrap.bind(el.getAttribute('data-shortcut'), function() {
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location.assign(el.getAttribute('href'));
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});
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}
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});
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</script>
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</body>
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</html>
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