Random projections: compress 10,000 dimensions to 30 by multiplying with random noise

Here is one of the most audacious results in machine learning: you can slash a dataset from thousands of dimensions down to a few dozen by multiplying it with a matrix of random numbers — and the geometry survives. No looking at the data, no eigenvectors, no training. Just draw a random linear map R and send every point x to (1/√k)·R·x . The pairwise distances between points barely change. The Johnson–Lindenstrauss lemma The licence for this is the Johnson–Lindenstrauss lemma. For any set of n…