Probabilistic Non-Negative Matrix Factorization with Binary Components

Non-negative matrix factorization is used to find a basic matrix and a weight matrix to approximate the non-negative matrix. It has proven to be a powerful low-rank decomposition technique for non-negative multivariate data. However, its performance largely depends on the assumption of a fixed number of features. This work proposes a new probabilistic non-negative matrix factorization which factorizes a non-negative matrix into a low-rank factor matrix with 0,1 constraints and a non-negative weight matrix. In order to automatically learn the potential binary features and feature number, a deterministic Indian buffet process variational inference is introduced to obtain the binary factor matrix. Further, the weight matrix is set to satisfy the exponential prior. To obtain the real posterior distribution of the two factor matrices, a variational Bayesian exponential Gaussian inference model is established. The comparative experiments on the synthetic and real-world datasets show the efficacy of the proposed method.