SKETCHING DISCRETE VALUED SPARSE MATRICES

Abstract

The problem of recovering a sparse matrix X from its sketch AXBT is referred to as the matrix sketching problem. Typically, the sketch is a lower dimensional matrix compared to X, and the sketching matrices A and B are known. Matrix sketching algorithms have been developed in the past to recover matrices from a continuous valued vectorspace (e.g., ℝN×N). However, employing such algorithms to recover discrete valued matrices may not be optimal. In this paper, we propose two novel algorithms that can efficiently recover a discrete valued sparse matrix from its sketch. We consider sparse matrices whose non-zero entries belong to a finite set. First, using the well known orthogonal matching pursuit (OMP), we present a matrix sketching algorithm. Second, we present a low-complexity message passing based recovery algorithm which exploits any sparsity structure that is present in X. Our simulation results verify that the proposed algorithms outperform the state-of-art matrix sketching algorithms in recovering discrete valued sparse matrices.