- Row Sampling by Lewis Weights
Authors: Michael B. Cohen, Richard Peng
Summary: We give a easy algorithm to effectively pattern the rows of a matrix whereas preserving the p-norms of its product with vectors. Given an n-by-d matrix A, we discover with excessive chance and in enter sparsity time an A′ consisting of about dlogd rescaled rows of A such that ∥Ax∥1 is near ∥A′x∥1 for all vectors x. We additionally present related outcomes for all ℓp that give practically optimum pattern bounds in enter sparsity time. Our outcomes are based mostly on sampling by “Lewis weights”, which will be considered as statistical leverage scores of a reweighted matrix. We additionally give an elementary proof of the ensures of this sampling course of for ℓ
