Non-negative Matrix Factorization with Quasi-Newton Optimization

摘要: Non-negative matrix factorization (NMF) is an emerging method with wide spectrum of potential applications in data analysis, feature extraction and blind source separation. Currently, most use relative simple multiplicative NMF learning algorithms which were proposed by Lee Seung, are based on minimization the Kullback-Leibler divergence Frobenius norm. Unfortunately, these relatively slow often need a few thousands iterations to achieve local minimum. In order increase convergence rate improve performance NMF, we more general cost function: so-called Amari alpha divergence. Taking into account special structure Hessian this function, derived second-order quasi-Newton for NMF. The validity algorithm has been extensively tested separation problems, both signals images. developed illustrated statistically dependent images from their linear mixtures.