Orthogonal Nonnegative Matrix Factorization by Sparsity and Nuclear Norm Optimization

Abstract

In this paper, we study orthogonal nonnegative matrix factorization. We demonstrate the coefficient matrix can be sparse and low-rank in the orthogonal nonnegative matrix factorization. By using these properties, we propose to use a sparsity and nuclear norm minimization for the factorization and develop a convex optimization model for finding the coefficient matrix in the factorization. Numerical examples including synthetic and real-world data sets are presented to illustrate the effectiveness of the proposed algorithm and demonstrate that its performance is better than other testing methods.