### 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 |
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Place of Publication | Birmingham |

Publisher | Aston University |

Number of pages | 13 |

ISBN (Print) | NCRG/97/010 |

Publication status | Published - 4 Sep 1997 |

### Keywords

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

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## Cite this

Tipping, M. E., & Bishop, C. M. (1997).

*Probabilistic principal component analysis*. Aston University.