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Mixtures of Probabilistic Principal Component Analysers (1998)
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| Citations: | 531 - 6 self |
BibTeX
@MISC{Tipping98mixturesof,
author = {Michael E. Tipping and Christopher M. Bishop},
title = {Mixtures of Probabilistic Principal Component Analysers},
year = {1998}
}
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Abstract
Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a maximum-likelihood framework, based on a specific form of Gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context of clustering, density modelling and local dimensionality reduction, and we demonstrate its applicat...
Keyphrases
probabilistic principal component analyser probability density ad hoc specific form pca model data complexity maximum-likelihood framework em algorithm previous attempt local dimensionality reduction conventional pca unique way well-defined mixture model local linear pca projection global linearity density modelling principal component analysis nonlinear variant popular technique mixture model gaussian latent variable model alternative paradigm
