Probabilistic principal component analysis

Michael E. Tipping; Christopher M. Bishop

doi:10.1111/1467-9868.00196

Probabilistic principal component analysis

Michael E. Tipping, Christopher M. Bishop

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	611-622
Number of pages	12
Journal	Journal of the Royal Statistical Society: series B
Volume	61
Issue number	3
DOIs	https://doi.org/10.1111/1467-9868.00196
Publication status	Published - 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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10.1111/1467-9868.00196

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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.",

keywords = "density estimation, EM algorithm, Gaussian mixtures, maximum likelihood, principal component analysis, probability model",

author = "Tipping, {Michael E.} and Bishop, {Christopher M.}",

note = "Published on behalf of the Royal Statistical Society.",

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AU - Bishop, Christopher M.

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KW - density estimation

KW - EM algorithm

KW - Gaussian mixtures

KW - maximum likelihood

KW - principal component analysis

KW - probability model

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JF - Journal of the Royal Statistical Society: series B

IS - 3

ER -

Probabilistic principal component analysis

Abstract

Bibliographical note

Keywords

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