Probabilistic Matrix Factorization for Data With Attributes Based on Finite Mixture Modeling.

Matrix factorization (MF) methods decompose a data matrix into a product of two-factor matrices (denoted as U and V ) which are with low ranks. In this article, we propose a generative latent variable model for the data matrix, in which each entry is assumed to be a Gaussian with mean to be the inner product of the corresponding columns of U and V . The prior of each column of U and V is assumed to be as a finite mixture of Gaussians. Further, we propose to model the attribute matrix with the data matrix jointly by considering them as conditional independence with respect to the factor matrix U , building upon previously defined model for the data matrix. Due to the intractability of the proposed models, we employ variational Bayes to infer the posteriors of the factor matrices and the clustering relationships, and to optimize for the model parameters. In our development, the posteriors and model parameters can be readily computed in closed forms, which is much more computationally efficient than existing sampling-based probabilistic MF models. Comprehensive experimental studies of the proposed methods on collaborative filtering and community detection tasks demonstrate that the proposed methods achieve the state-of-the-art performance against a great number of MF-based and non-MF-based algorithms.