Bayesian Adaptive Matrix Factorization With Automatic Model Selection

Low-rank matrix factorization has long been recognized as a fundamental problem in many computer vision applications. Nevertheless, the reliability of existing matrix factorization methods is often hard to guarantee due to challenges brought by such model selection issues as selecting the noise model and determining the model capacity. We address these two issues simultaneously in this paper by proposing a robust non-parametric Bayesian adaptive matrix factorization (AMF) model. AMF proposes a new noise model built on the Dirichlet process Gaussian mixture model (DP-GMM) by taking advantage of its high flexibility on component number selection and capability of fitting a wide range of unknown noise. AMF also imposes an automatic relevance determination (ARD) prior on the low-rank factor matrices so that the rank can be determined automatically without the need for enforcing any hard constraint. An efficient variational method is then devised for model inference. We compare AMF with state-of-the-art matrix factorization methods based on data sets ranging from synthetic data to real-world application data. From the results, AMF consistently achieves better or comparable performance.