CiteSeerX — Probabilistic Principal Component Analysis

Probabilistic Principal Component Analysis (1999) [248 citations — 5 self]

Popular Tags

No tags have been applied to this document.

BibTeX | Add To MetaCart

@ARTICLE{Tipping99probabilisticprincipal,
    author = {Michael E. Tipping and Chris M. Bishop},
    title = {Probabilistic Principal Component Analysis},
    journal = {Journal of the Royal Statistical Society, Series B},
    year = {1999},
    volume = {61},
    pages = {611--622}
}

Years of Citing Articles

Bookmarks

OpenURL

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 iteratively, and discuss, with illustrative examples, the advantages conveyed by this probabilistic approach to PCA. Keywords: Principal component analysis

Citations

970	Principal Component Analysis – Jolliffe - 1986
767	Pattern recognition and Neural Networks – Ripley - 1996
507	Statistical Analysis with Missing Data – Little, Rubin - 2002
416	Statistical Analysis of Finite Mixture Distributions – Titterington, Smith, et al. - 1985
239	Analysis of a Complex of Statistical Variables into Principal Components – Hotelling - 1993
101	On lines and planes of closest fit to systems of points in space – Pearson - 1901
97	Latent Variable Models and Factor Analysis – Bartholomew - 1987
71	A hierarchical latent variable model for data visualization – Bishop, Tipping - 1998
70	EM algorithms for ML factor analysis – Rubin, Thayer - 1982
54	Asymptotic theory for principal component analysis – Anderson - 1963
47	Statistical Factor Analysis and Related Methods – Basilevsky - 1994
42	Statistical inference in factor analysis – Anderson, Rubin - 1956
33	Optimally adaptive transform coding – Dony, Haykin - 1995
12	On principal components and least square methods of factor analysis – WHITTLE - 1952
10	Multivariate Analysis Part 2: Classification, Covariance Structures and Repeated Measurements – Krzanowski, Marriott - 1994
9	Maximum likelihood estimation and factor analysis – Young - 1940
7	A modified method of estimation in factor analysis and some large sample results – Lawley - 1953