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Probabilistic Principal Component Analysis
Article first published online: 6 JAN 2002
DOI: 10.1111/1467-9868.00196
1999 Royal Statistical Society
Issue
1467-9868/asset/cover.gif?v=1&s=be03fd3eafae344cc2a65cd9ee0ea5397cc00b51 "Journal of the Royal Statistical Society: Series B (Statistical Methodology)")
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Volume 61, Issue 3, pages 611–622, 1999
Additional Information
How to Cite
Tipping, M. E. and Bishop, C. M. (1999), Probabilistic Principal Component Analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61: 611–622. doi: 10.1111/1467-9868.00196
Publication History
- Issue published online: 6 JAN 2002
- Article first published online: 6 JAN 2002
- Abstract
- Cited By
Keywords:
- Density estimation;
- EM algorithm;
- Gaussian mixtures;
- Maximum likelihood;
- Principal component analysis;
- Probability model
Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based on a probability model. 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 that is 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.