Categorical variables in distance computations
<p>Doing this mapping results in a dimensional expansion of the problem space (3 dimensions instead of 1), though those dimensions are flatter. Well, the dimensions are not flatter; those are flat by definition. But the geometry of the problem is (flatter). We like to think of this as <em>unwrapping</em> a categorical variable into higher dimensions.</p>
<p>This dimensional expansion can become a problem if we have many categorical variables and/or many categories per variable. We might expand the problem’s dimensions so much that we end up with the number of (new) variables greater than the number of data points… which is tractable, but less than ideal.</p>
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