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, say p features, where p is 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.