Electronic Journal of Statistics

Functional principal components analysis via penalized rank one approximation

Jianhua Z. Huang, Haipeng Shen, and Andreas Buja

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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.

Article information

Electron. J. Statist., Volume 2 (2008), 678-695.

First available in Project Euclid: 30 July 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression 62H25: Factor analysis and principal components; correspondence analysis
Secondary: 65F30: Other matrix algorithms

Functional data analysis penalization regularization singular value decomposition


Huang, Jianhua Z.; Shen, Haipeng; Buja, Andreas. Functional principal components analysis via penalized rank one approximation. Electron. J. Statist. 2 (2008), 678--695. doi:10.1214/08-EJS218. https://projecteuclid.org/euclid.ejs/1217450800

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