Probabilistic principal component analysis

doi:10.1111/1467-9868.00196

Probabilistic principal component analysis

2002-01-06

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DOI：10.1111/1467-9868.00196

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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.

Keyword:

density estimation

EM algorithm

Gaussian mixtures

maximum likelihood

principal component analysis

probability model

Probabilistic principal component analysis

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