Probabilistic principal component analysis

Michael E. Tipping, Christopher M. Bishop

    Research output: Contribution to journalArticle

    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 the advantages conveyed by the definition of a probability density function for 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 - Oct 1999

    Bibliographical note

    Published on behalf of the Royal Statistical Society.

    Keywords

    • density estimation
    • EM algorithm
    • Gaussian mixtures
    • maximum likelihood
    • principal component analysis
    • probability model

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