Probabilistic principal component analysis

Michael Tipping, Christopher Bishop

Research output: Contribution to journalArticlepeer-review

2696 Citations (SciVal)

Abstract

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based on a probability model. 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 that is 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
JournalJournal of the Royal Statistical Society: Series B - Statistical Methodology
Volume61
Issue number3
Publication statusPublished - Sept 1999

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