Adaptive computation of the Symmetric Nonnegative Matrix Factorization (SymNMF)

Abstract

Symmetric Nonnegative Matrix Factorization (SymNMF) provides a symmetric nonnegative low rank decomposition of symmetric matrices. It has found application in several domains such as data mining, bioinformatics and graph clustering. In this paper SymNMF is obtained by solving a penalized nonsymmetric minimization problem. Instead of letting the penalizing parameter increase according to an a priori fixed rule, as suggested in literature, we propose a heuristic approach based on an adaptive technique. The factorization is performed by applying, as inner-outer procedure, the Alternating Nonnegative Least Squares (ANLS). The inner problems are solved by two nonnegative quadratic optimization methods: an Active-Set-like method (BPP) and the Greedy Coordinate Descent method (GCD). Extensive experimentation shows that the proposed heuristic approach is effective with both the inner methods, GCD outperforming BPP in terms of computational time complexity.