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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An approach to non-linear principal components analysis using radially symmetric kernel functions
TL;DR: An approach to non-linear principal components using radially symmetric kernel basis functions is described and can be related to the homogeneity analysis approach of Gifi through the minimization of a loss function.
Proceedings Article
A Neural Network Autoassociator for Induction Motor Failure Prediction
Thomas Petsche,Angelo R. Marcantonio,Christian Darken,Stephen José Hanson,Gary M. Kuhn,N. Iwan Santoso +5 more
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Local models and Gaussian mixture models for statistical data processing
TL;DR: Local models or Gaussian mixture models can be efficient tools for dimension reduction, exploratory data analysis, feature extraction, classification and regression, and proposed algorithms for regularizing them are presented.
Journal ArticleDOI
Bayesian Analysis of Mixtures of Factor Analyzers
Akio Utsugi,Toru Kumagai +1 more
TL;DR: For Bayesian inference on the mixture of factor analyzers, natural conjugate priors on the parameters are introduced, and then a Gibbs sampler that generates parameter samples following the posterior is constructed, regarded as a maximum a posteriori estimation algorithm with hyperparameter search.
Journal ArticleDOI
The Bayesian Evidence Scheme for Regularizing Probability-Density Estimating Neural Networks
TL;DR: A regularization method for mixture models with generalized linear kernel centers is proposed, which adopts the Bayesian evidence approach and optimizes the hyperparameters of the prior by type II maximum likelihood.