Two fast vector-wise update algorithms for orthogonal nonnegative matrix factorization with sparsity constraint

Abstract

Recently, orthogonal nonnegative matrix factorization (ONMF) has been introduced and shown to work remarkably well for clustering tasks. Because of the nonnegativity and the orthogonality constraints, the orthogonal factor matrix of ONMF is naturally sparse. Based on this fact, by introducing sparsity constraints on the orthogonal coefficient matrix, we propose two vector-wise algorithms based on Hierarchical Alternating Least Squares (HALS) and Block Prox-linear (BPL) methods to the approximately sparse orthogonal nonnegative matrix factorization (SONMF). Some global convergence results are established under the mild conditions. Numerical results including synthetic and real-world datasets are given to illustrate that the proposed algorithms compute highly accurate values and perform better than the other testing ONMF methods.