Electronic Journal of Statistics

Functional principal components analysis via penalized rank one approximation

Jianhua Z. Huang, Haipeng Shen, and Andreas Buja

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 30 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1217450800

Digital Object Identifier
doi:10.1214/08-EJS218

Mathematical Reviews number (MathSciNet)
MR2426107

Zentralblatt MATH identifier
1320.62097

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

Keywords
Functional data analysis penalization regularization singular value decomposition

Citation

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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