A low-cost variational-Bayes technique for merging mixtures of probabilistic principal component analyzers

Mixtures of probabilistic principal component analyzers (MPPCA) have shown effective for modeling high-dimensional data sets living on non-linear manifolds. Briefly stated, they conduct mixture model estimation and dimensionality reduction through a single process. This paper makes two contributions: first, we disclose a Bayesian technique for estimating such mixture models. Then, assuming several MPPCA models are available, we address the problem of aggregating them into a single MPPCA model, which should be as parsimonious as possible. We disclose in detail how this can be achieved in a cost-effective way, without sampling nor access to data, but solely requiring mixture parameters. The proposed approach is based on a novel variational-Bayes scheme operating over model parameters. Numerous experimental results and discussion are provided.