As the dimension increases, more space(or volume) will concentrate on the surface or corner of the total space, and most of the sample vectors will be orthogonal to each other at 10:34, Thanks for your great explanation!
Is the max/min ratio plot based on draws from the a multivariate gaussian with increasing dimensions? Background: I tried to replicate this for a class of mine with a multivariate gaussian but somehow it doesn't converge as nicely as your plot. Could be a plotting issue tho. After 500 iteratios I have a ratio of 2.711633 based on eucledian distance.
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The "wee..." alone deserves a million likes!😂
Such a great explanation! Thanks a lot
Great video. Could you explain more why all of the volume of the hypercube is contained in the corners as the dimensions grow?
As the dimension increases, more space(or volume) will concentrate on the surface or corner of the total space, and most of the sample vectors will be orthogonal to each other at 10:34, Thanks for your great explanation!
the best explanation! thanks!
Is the max/min ratio plot based on draws from the a multivariate gaussian with increasing dimensions? Background: I tried to replicate this for a class of mine with a multivariate gaussian but somehow it doesn't converge as nicely as your plot. Could be a plotting issue tho. After 500 iteratios I have a ratio of 2.711633 based on eucledian distance.
Intuitionally explained!
Are 3 and 4 dimension somehow special?