Journal ArticleDOI
Mixtures of probabilistic principal component analyzers
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TLDR
PCA is formulated within a maximum likelihood framework, based on a specific form of gaussian latent variable model, which leads to a well-defined mixture model for probabilistic principal component analyzers, whose parameters can be determined using an expectation-maximization algorithm.Abstract:
Principal component analysis (PCA) is one of the most popular techniques for processing, compressing, and visualizing 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. Therefore, previous attempts to formulate mixture models for PCA have been ad hoc to some extent. In this article, 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 analyzers, whose parameters can be determined using an expectationmaximization algorithm. We discuss the advantages of this model in the context of clustering, density modeling, and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.read more
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References
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Maximum likelihood from incomplete data via the EM algorithm
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Neural Networks for Pattern Recognition
Suresh Kothari,Heekuck Oh +1 more
TL;DR: The chapter discusses two important directions of research to improve learning algorithms: the dynamic node generation, which is used by the cascade correlation algorithm; and designing learning algorithms where the choice of parameters is not an issue.
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LIII. On lines and planes of closest fit to systems of points in space
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