Probabilistic principal component analysis

Michael E. Tipping, Christopher M. Bishop

    Research output: Preprint or Working paperTechnical report


    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
    Place of PublicationBirmingham
    PublisherAston University
    Number of pages13
    ISBN (Print)NCRG/97/010
    Publication statusPublished - 4 Sept 1997


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


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