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Biometrika 1999 86(4):899-908; doi:10.1093/biomet/86.4.899
© 1999 by Biometrika Trust
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Partial common principal component subspaces

JR Schott

Department of Statistics, University of Central Florida, Orlando, FL 32816-2370, USA E-mail: jschott@pegasus.cc.ucf.edu

We consider the principal components analysis of g groups of m variables for those situations in which, for each group, the first k principal components account for most of the total variability of observations in that group. If the set of these gk principal component vectors spans a space of dimension r, where r is less than m, then it will be possible simultaneously to reduce the dimensionality, for all groups, from m to r while retaining most of the within-group variability. Methods are already available for determining if r=k, in which case the g groups have a common principal component subspace. In this paper, we develop a general procedure for determining if r=s for arbitrary s. This can then be used repeatedly to determine r when r>k.

Key Words: dimensionality reduction; principal components analysis


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R. D. Cook and L. Forzani
Covariance reducing models: An alternative to spectral modelling of covariance matrices
Biometrika, December 1, 2008; 95(4): 799 - 812.
[Abstract] [PDF]


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