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<title>Brandon Rozek</title>
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<h1>Why use different distance measures?</h1>
<p>I made an attempt to find out in what situations people use different distance measures. Looking around in the Internet usually produces the results &quot;It depends on the problem&quot; or &quot;I typically just always use Euclidean&quot;</p>
<p>Which as you might imagine, isn't a terribly useful answer. Since it doesn't give me any examples of which types of problems different distances solve.</p>
<p>Therefore, let's think about it in a different way. What properties do different distance measures have that make them desirable?</p>
<h2>Manhattan Advantages</h2>
<ul>
<li>The gradient of this function has a constant magnitude. There's no power in the formula</li>
<li>Unusual values affect distances on Euclidean more since the difference is squared</li>
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<p><a href="https://datascience.stackexchange.com/questions/20075/when-would-one-use-manhattan-distance-as-opposite-to-euclidean-distance">https://datascience.stackexchange.com/questions/20075/when-would-one-use-manhattan-distance-as-opposite-to-euclidean-distance</a></p>
<h2>Mahalanobis Advantages</h2>
<p>Variables can be on different scales. The Mahalanobis formula has a built in variance-covariance matrix which allows you to rescale your variables to make distances of different variables more comparable.</p>
<p><a href="https://stats.stackexchange.com/questions/50949/why-use-the-mahalanobis-distance#50956">https://stats.stackexchange.com/questions/50949/why-use-the-mahalanobis-distance#50956</a></p>
<h2>Euclidean Disadvantages</h2>
<p>In higher dimensions, the points essentially become uniformly distant from one another. This is a problem observed in most distance metrics but it's more obvious with the Euclidean one.</p>
<p><a href="https://stats.stackexchange.com/questions/99171/why-is-euclidean-distance-not-a-good-metric-in-high-dimensions/">https://stats.stackexchange.com/questions/99171/why-is-euclidean-distance-not-a-good-metric-in-high-dimensions/</a></p>
<p>Hopefully in this course, we'll discover more properties as to why it makes sense to use different distance measures since it can have a impact on how our clusters are formed.</p>
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