Simplicial Nonnegative Matrix Tri-factorization: Fast Guaranteed Parallel Algorithm

Abstract

Nonnegative matrix factorization (NMF) is a linear powerful dimension reduction and has various important applications. However, existing models remain the limitations in the terms of interpretability, guaranteed convergence, computational complexity, and sparse representation. In this paper, we propose to add simplicial constraints to the classical NMF model and to reformulate it into a new model called simplicial nonnegative matrix tri-factorization to have more concise interpretability via these values of factor matrices. Then, we propose an effective algorithm based on a combination of three-block alternating direction and Frank-Wolfe’s scheme to attain linear convergence, low iteration complexity, and easily controlled sparsity. The experiments indicate that the proposed model and algorithm outperform the NMF model and its state-of-the-art algorithms.