Learning latent features with infinite non-negative binary matrix tri-factorization

Abstract

Non-negative Matrix Factorization (NMF) has been widely exploited to learn latent features from data. However, previous NMF models often assume a fixed number of features, saypfeatures, wherepis simply searched by experiments. Moreover, it is even difficult to learn binary features, since binary matrix involves more challenging optimization problems. In this paper, we propose a new Bayesian model called infinite non-negative binary matrix tri-factorizations model (iNBMT), capable of learning automatically the latent binary features as well as feature number based on Indian Buffet Process (IBP). Moreover, iNBMT engages a tri-factorization process that decomposes a nonnegative matrix into the product of three components including two binary matrices and a non-negative real matrix. Compared with traditional bi-factorization, the tri-factorization can better reveal the latent structures among items (samples) and attributes (features). Specifically, we impose an IBP prior on the two infinite binary matrices while a truncated Gaussian distribution is assumed on the weight matrix. To optimize the model, we develop an efficient modified maximization-expectation algorithm (ME-algorithm), with the iteration complexity one order lower than another recently-proposed Maximization-Expectation-IBP model[9]. We present the model definition, detail the optimization, and finally conduct a series of experiments. Experimental results demonstrate that our proposed iNBMT model significantly outperforms the other comparison algorithms in both synthetic and real data.