Spherical Matrix Factorization

Abstract

Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis. In this paper, we propose a method by adding constraints on factors to unify the Euclidean and angle distance. However, due to non-convexity of the objective and constraints, the optimized solution is not easy to obtain. In this paper we propose a general framework to systematically solve it with provable convergence guarantee with various constraints.