Matrix Decompositions using sub-Gaussian Random Matrices

Abstract: In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian matrix with large probability to have zero entries is metric conserving. We also present a new algorithm, which achieves with high probability, a rank $r$ decomposition approximation for an $m \times n$ matrix that has an asymptotic complexity like state-of-the-art algorithms. We derive an error bound that does not depend on the first $r$ singular values. Although the proven error bound is not as tight as the state-of-the-art bound, experiments show that the proposed algorithm is faster in practice, while getting the same error rates as the state-of-the-art algorithms get.