Multiplicative Update for Projective Nonnegative Matrix Factorization with Bregman Divergence

Nonnegative Matrix Factorization (NMF) has been widely used in dimensionality reduction, machine learning, and data mining, etc. It aims to find two nonnegative matrices whose product can well approximate the nonnegative data matrix, which naturally lead to parts-based representation. In this paper, we present a family of projective nonnegative matrix factorization algorithm, PNMF with Bregman divergence. Several versions of divergence such as Euclidean distance and Kullback-Leibler (KL) divergence with PNMF have been studied. In this paper, we investigate the MU rules to solve the PNMF with some other divergence, such as β-divergence, IS-divergence. It has been shown that the base matrix by Bregman PNMF is better suitable for orthoganal, localized and sparse representation than by traditional NMF.