MML Probabilistic Principal Component Analysis

Principal component analysis (PCA) is perhaps the most widely method for data dimensionality reduction. A key question in PCA decomposition of data is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting the number of principal compoents based on the Bayesian minimum message length method of inductive inference. We also derive a new estimate of the isotropic residual variance and demonstrate, via numerical experiments, that it improves on the usual maximum likelihood approach.