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Johnson–Lindenstrauss distortion

Pairwise distance distortion under a random Gaussian projection, as a function of the target dimension k.

High-Dim Probabilityjohnson-lindenstraussrandom projectiondimension reductionembeddings

The mathematics behind this

The Johnson–Lindenstrauss Lemma
A complete proof that random projection to O(log N / eps^2) dimensions preserves all pairwise distances, with the dimension requirement, the geometry and the limits of the result.

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