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You can extend these triangles and tetrahedral analyses into higher dimensional simplexes, which give insights into structure of categorical probability distrib
by j7ake 5y ago
You can extend these triangles and tetrahedral analyses into higher dimensional simplexes, which give insights into structure of categorical probability distributions as number of categories increases.
One interesting property is that the volume of the simplex goes something like 1 / n!, which breaks a lot of intuition of what happens as n gets large.
- moonchild 5y agoIt was pointed out recently (I think in the 'high-dimensional space is pointy' thread) that in high dimensions, the (n-d hyper)cube may not be the most meaningful measure of volume (and that euclidean distance may not be the most meaningful measure of distance).