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

MML Probabilistic Principal Component Analysis