### Abstract

Original language | English |
---|---|

Place of Publication | Birmingham |

Publisher | Aston University |

Number of pages | 13 |

ISBN (Print) | NCRG/97/010 |

Publication status | Published - 4 Sep 1997 |

### Fingerprint

### Keywords

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

### Cite this

*Probabilistic principal component analysis*. Birmingham: Aston University.

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

Research output: Working paper › Technical report

TY - UNPB

T1 - Probabilistic principal component analysis

AU - Tipping, Michael E.

AU - Bishop, Christopher M.

PY - 1997/9/4

Y1 - 1997/9/4

N2 - 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.

AB - 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.

KW - density estimation

KW - EM algorithm

KW - Gaussian mixtures

KW - maximum likelihood

KW - principal component analysis

KW - probability model

M3 - Technical report

SN - NCRG/97/010

BT - Probabilistic principal component analysis

PB - Aston University

CY - Birmingham

ER -