Re:Gaussian Distributions Are Soap Bubbles
by ks1723 on Saturday November 11, 2017 @03:03PM
(#15677867)
What i found quite surprising in that context, is that the volume of the n-dimensional ball for any finite fixed radius goes to zero as n goes to infinity (see, for example, section "high dimensions" of https://en.m.wikipedia.org/wiki/Volume_of_an_n-ball)
Re:Gaussian Distributions Are Soap Bubbles
by cs702 on Saturday November 11, 2017 @03:13PM
(#15677914)
There are multiple good (intuitive) explanations for this here: https://math.stackexchange.com/questions/67039/why-does-volu...
More precisely: it is the mass that is “concentrated” at the edge, not the density. In the Gaussian case the distribution “gets more and more dense in the middle” regardless of the number of dimensions. However, in high dimensions the volume in the middle is so low that essentially all the mass is close to the surface of the hypersphere.