random-projection-jl-lemma-bound

Summary

You can shrink a very high-dimensional dataset down to a small number of dimensions and still keep the distances between all points roughly intact, as long as the number of points isn't too large and you don't demand perfect precision. This is the mathematical reason behind most practical dimensionality-reduction and nearest-neighbor techniques in machine learning, since it guarantees that a compact representation won't silently distort the structure of the data.