Probabilistic principal component analysis

Michael E. Tipping, Christopher M. Bishop

    Research output: Working paperTechnical report

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

    Fingerprint

    Probabilistic Analysis
    Principal Component Analysis
    Latent Variable Models
    Probability Model
    EM Algorithm
    Factor Analysis
    Likelihood Function
    Maximum Likelihood Estimation
    Probability density function
    Data analysis
    Subspace
    Demonstrate

    Keywords

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

    Cite this

    Tipping, M. E., & Bishop, C. M. (1997). Probabilistic principal component analysis. Birmingham: Aston University.
    Tipping, Michael E. ; Bishop, Christopher M. / Probabilistic principal component analysis. Birmingham : Aston University, 1997.
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    Tipping, ME & Bishop, CM 1997 'Probabilistic principal component analysis' Aston University, Birmingham.

    Probabilistic principal component analysis. / Tipping, Michael E.; Bishop, Christopher M.

    Birmingham : Aston University, 1997.

    Research output: Working paperTechnical report

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    KW - Gaussian mixtures

    KW - maximum likelihood

    KW - principal component analysis

    KW - probability model

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    Tipping ME, Bishop CM. Probabilistic principal component analysis. Birmingham: Aston University. 1997 Sep 4.