Johnson–Lindenstrauss lemma

Can you fit more clothes in a drawer without folding them?

Imagine you have a drawer full of clothes, but it's getting too crowded. You want to fit more clothes without folding them to save space.

Think of your clothes as points in a high-dimensional space. The Johnson-Lindenstrauss lemma is like finding a smaller drawer (lower-dimensional space) where you can still see your clothes (points) almost the same way they looked before.

Example

If you have 100 clothes (points) in a drawer (high-dimensional space), you can find a smaller drawer (lower-dimensional space) with just 10 clothes (points) that still look almost the same (preserve distances).

Remember this

The Johnson-Lindenstrauss lemma helps you reduce the space you need (dimensionality) while keeping your clothes (data points) looking almost the same (preserve pairwise distances).

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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