Probabilistic Principal Component Analysis

Michael E. Tipping, Christopher M. Bishop

Research output: Contribution to journalArticlepeer-review

Abstract

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss, with illustrative examples, the advantages conveyed by this probabilistic approach to PCA.
Original languageEnglish
Pages (from-to)611-622
Number of pages12
JournalJournal of the Royal Statistical Society: Series B
Volume61
Issue number3
DOIs
Publication statusPublished - 1999

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