Convergence-guaranteed multiplicative algorithms for nonnegative matrix factorization with β-divergence

Abstract

This paper presents a new multiplicative algorithm for nonnegative matrix factorization with β-divergence. The derived update rules have a similar form to those of the conventional multiplicative algorithm, only differing through the presence of an exponent term depending on β. The convergence is theoretically proven for any real-valued β based on the auxiliary function method. The convergence speed is experimentally investigated in comparison with previous works.