Adaptive Multiplicative Updates for Projective Nonnegative Matrix Factorization

Projective Nonnegative Matrix Factorization (PNMF) is able to extract sparse features and provide good approximation for discrete problems such as clustering. However, the original PNMF optimization algorithm can not guarantee theoretical convergence during the iterative learning. We propose here an adaptive multiplicative algorithm for PNMF which is not only theoretically convergent but also significantly faster than the previous implementation. An adaptive exponent scheme has been adopted for our method instead of the old unitary one, which ensures the theoretical convergence and accelerates the convergence speed thanks to the adaptive exponent. We provide new multiplicative update rules for PNMF based on the squared Euclidean distance and the I-divergence. For the empirical contributions, we first provide a counter example on the monotonicity using the original PNMF algorithm, and then verify our proposed method by experiments on a variety of real-world data sets.