Now that we’ve had a glimpse of what it means to analyze data sets in different dimensions, we should take a little detour to consider really high dimensional data. In the discussion of regression, I suggested using your intuition about planes in three-dimensional space to understand hyperplanes in higher dimensions. This is a great way to get around the fact that we can’t visualize dimensions higher than three, but we still have to be careful to understand how geometry in higher dimensions is different from geometry in two or three dimensions. As it turns out, a number of aspects of higher dimensional geometry are quite counter-intuitive and this is a major component of what’s called the curse of dimensionality.
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