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Probabilistic Principal Component Analysis
Author(s) -
Tipping Michael E.,
Bishop Christopher M.
Publication year - 1999
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00196
Subject(s) - principal component analysis , probabilistic logic , subspace topology , likelihood function , computer science , latent variable , statistical model , set (abstract data type) , latent variable model , sparse pca , data set , maximum likelihood , pattern recognition (psychology) , factor analysis , artificial intelligence , mathematics , data mining , statistics , programming language
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.