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I have a question about Johnson-Lindenstrauss and k-means.

I m study a resource that explain a link between Johnson-Lindenstrauss and k-means. From what I understand, Johnson-Lindenstrauss helps us to validate k-mean, saying that if projected into another space, the points maintain the distance with a small error (approximation).

Can someone explain this concept to me in a simpler way? Or give me some resources?

I also read the paper, Database-friendly random projections: Johnson-Lindenstrauss with binary coins by Dimitris Achlioptas, which tried to tie everything to a sphere, but I got lost.

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