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