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Counterintuitive Properties of High Dimensional Space (2018)

(people.eecs.berkeley.edu)
247 points nabla9 | 3 comments | 13 Oct 24 21:09 UTC | HN request time: 0.397s | source
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mattxxx ◴[14 Oct 24 00:16 UTC] No.41832925[source]▶
Yea - high dimensional spaces are weird and hard to reason about... and we're working very frequently in them, especially when dealing with ML.
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l33t7332273 ◴[14 Oct 24 01:17 UTC] No.41833261[source]▶
Luckily if you do enough math it becomes much easier to reason about such spaces
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1. JBiserkov ◴[14 Oct 24 02:55 UTC] No.41833809[source]▶
- How do you even visualize an 11-dimensional space?

- oh that's easy - you just visualize an N-dimensional space and then set N equal to 11.

replies(2): >>41833988 #>>41833998 #
2. rectang ◴[14 Oct 24 03:44 UTC] No.41833988[source]▶
I think of high-dimensional spaces in terms of projection. Projecting a 3-dimensional space onto a 2-dimensional space loses information and the results depend on perspective. Same with an 11-dimensional space being projected onto a 10-dimensional space.

I find that this metaphor works pretty well for visualizing how a vector-space search engine represents how two documents can be "similar" in N-dimensional term-space: look at them from the right angle and they appear close together.

3. marcosdumay ◴[14 Oct 24 03:46 UTC] No.41833998[source]▶
Yeah, stopping that need to visualize everything is one of the mechanisms usually adopted for working in high-dimensional space.