Variational Bayesian Approach to Canonical Correlation Analysis

As a dimension reduction algorithm, canonical correlation analysis (CCA) encounters the issue of selecting the number of canonical correlations. In this letter, we present a Bayesian model selection algorithm for CCA based on a probabilistic interpretation. A hierarchical Bayesian model is applied to probabilistic CCA and learned by variational approximation. This method not only estimates the model parameters, but also automatically determines the number of canonical correlations and avoids overfitting. Experiments show that it performs better compared with maximum likelihood and some other model selection methods.