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Counterintuitive Properties of High Dimensional Space (2018)

(people.eecs.berkeley.edu)
247 points nabla9 | 1 comments | 13 Oct 24 21:09 UTC | HN request time: 0.215s | source
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remcob ◴[14 Oct 24 04:17 UTC] No.41834128[source]▶
The distance between two uniform random points on an n-sphere clusters around the equator. The article shows a histogram of the distribution in fig. 11. While it looks Gaussian, it is more closely related to the Beta distribution. I derived it in my notes, as (surprisingly) I could not find it easily in literature:

https://xn--2-umb.com/21/n-sphere

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zombot ◴[14 Oct 24 06:01 UTC] No.41834640[source]▶
> The distance between two uniform random points on an n-sphere clusters around the equator.

This sentence makes no sense to me.

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p1esk ◴[14 Oct 24 06:20 UTC] No.41834728[source]▶
He means it clusters around the distance from a pole to the equator.
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1. remcob ◴[14 Oct 24 06:50 UTC] No.41834887[source]▶
Correct. I was too short in my comment. It's explained in the article: without loss of generality you can call one of the two points the 'north pole' and then the other one will be distributed close to the equator.