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Abstract: Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper 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 closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace... (Update)
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BibTeX entry: (Update)
Michael Tipping and Christopher Bishop. Probabilistic principal component analysis. Technical Report NCRG/97/010, Neural Computing Research Group, Aston University, September 1997. http://citeseer.ist.psu.edu/article/tipping97probabilistic.html More
@misc{ tipping97probabilistic,
author = "M. Tipping and C. Bishop",
title = "Probabilistic principal component analysis",
text = "Michael Tipping and Christopher Bishop. Probabilistic principal component
analysis. Technical Report NCRG/97/010, Neural Computing Research Group,
Aston University, September 1997.",
year = "1997",
url = "citeseer.ist.psu.edu/article/tipping97probabilistic.html" }
Citations (may not include all citations):2528 Maximum likelihood from incomplete data via the EM algorithm (context) - Dempster, Laird et al. - 1977
1662 Neural Networks for Pattern Recognition (context) - Bishop - 1995
121 Analysis of a complex of statistical variables into principa.. (context) - Hotelling - 1933
64 EM algorithms for ML factor analysis (context) - Rubin, Thayer - 1982
45 Latent Variable Models and Factor Analysis (context) - Bartholomew - 1987
36 Introduction to Multivariate Analysis (context) - Chatfield, Collins - 1980
28 On lines and planes of closest fit to systems of points in s.. (context) - Pearson - 1901
23 Statistical Factor Analysis and Related Methods - Basilevsky - 1994
22 Asymptotic theory for principal component analysis (context) - Anderson - 1963
12 Mixtures of principal component analysers (context) - Tipping, Bishop
2 Principal Component Analysis (context) - Educational, -- - 1986
2 Multivariate Analysis Part I: Distributions (context) - Krzanowski, Marriott - 1994
2 Hierarchical models for data visualization (context) - Tipping, Bishop
1 Estimation and tests of significance in factor analysis (context) - Rao - 1955
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