Low-Rank Approximations with Sparse Factors I: Basic Algorithms and Error Analysis

Abstract

We consider the problem of computing low-rank approximations of matrices. The novel aspects of our approach are that we require the low-rank approximations to be written in a factorized form with sparse factors, and the degree of sparsity of the factors can be traded off for reduced reconstruction error by certain user-determined parameters. We give a detailed error analysis of our proposed algorithms and compare the computed sparse low-rank approximations with those obtained from singular value decomposition. We present numerical examples arising from some application areas to illustrate the efficiency and accuracy of our algorithms.