Open Access
2008 Functional principal components analysis via penalized rank one approximation
Jianhua Z. Huang, Haipeng Shen, Andreas Buja
Electron. J. Statist. 2: 678-695 (2008). DOI: 10.1214/08-EJS218


Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we propose an alternative approach to FPCA using penalized rank one approximation to the data matrix. Our contributions are four-fold: (1) by considering invariance under scale transformation of the measurements, the new formulation sheds light on how regularization should be performed for FPCA and suggests an efficient power algorithm for computation; (2) it naturally incorporates spline smoothing of discretized functional data; (3) the connection with smoothing splines also facilitates construction of cross-validation or generalized cross-validation criteria for smoothing parameter selection that allows efficient computation; (4) different smoothing parameters are permitted for different FPCs. The methodology is illustrated with a real data example and a simulation.


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Jianhua Z. Huang. Haipeng Shen. Andreas Buja. "Functional principal components analysis via penalized rank one approximation." Electron. J. Statist. 2 678 - 695, 2008.


Published: 2008
First available in Project Euclid: 30 July 2008

zbMATH: 1320.62097
MathSciNet: MR2426107
Digital Object Identifier: 10.1214/08-EJS218

Primary: 62G08 , 62H25
Secondary: 65F30

Keywords: Functional data analysis , Penalization , regularization , Singular value decomposition

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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