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Probabilistic Principal Component Analysis (1999)
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| Venue: | JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B |
| Citations: | 709 - 5 self |
BibTeX
@ARTICLE{Tipping99probabilisticprincipal,
author = {Michael E. Tipping and Chris M. Bishop},
title = {Probabilistic Principal Component Analysis},
journal = {JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B},
year = {1999},
volume = {61},
number = {3},
pages = {611--622}
}
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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, with illustrative examples, the advantages conveyed by this probabilistic approach to PCA.
Keyphrases
probabilistic principal component analysis principal component analysis latent variable model principal ax factor analysis data analysis observed data vector ubiquitous technique maximum-likelihood estimation principal subspace illustrative example probabilistic approach em algorithm likelihood function probability model
