Bayesian Joint Matrix Decomposition for Data Integration with Heterogeneous Noise

Matrix decomposition is a popular and fundamental approach in machine learning data mining. It has been successfully applied into various fields. Most matrix methods focus on decomposing from one single source. However, it common that are different sources with heterogeneous noise. A few of the have extended for such multi-view integration pattern discovery while only were designed to consider heterogeneity noise explicitly. To this end, article, we propose joint framework (BJMD), which models by Gaussian distribution Bayesian framework. We develop two algorithms solve model: variational inference algorithm, makes full use posterior distribution; another maximum more scalable can be easily paralleled. Extensive experiments synthetic real-world datasets demonstrate BJMD superior or competitive state-of-the-art methods.