Statistics Papers

Document Type

Journal Article

Date of this Version

2009

Publication Source

Journal of the American Statistical Association

Volume

104

Issue

488

Start Page

1609

Last Page

1620

DOI

10.1198/jasa.2009.tm08024

Abstract

Two-way functional data consist of a data matrix whose row and column domains are both structured, for example, temporally or spatially, as when the data are time series collected at different locations in space. We extend one-way functional principal component analysis (PCA) to two-way functional data by introducing regularization of both left and right singular vectors in the singular value decomposition (SVD) of the data matrix. We focus on a penalization approach and solve the nontrivial problem of constructing proper two-way penalties from one-way regression penalties. We introduce conditional cross-validated smoothing parameter selection whereby left-singular vectors are cross-validated conditional on right-singular vectors, and vice versa. The concept can be realized as part of an alternating optimization algorithm. In addition to the penalization approach, we briefly consider two-way regularization with basis expansion. The proposed methods are illustrated with one simulated and two real data examples. Supplemental materials available online show that several “natural” approaches to penalized SVDs are flawed and explain why so.

Copyright/Permission Statement

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 01 Jan 2012, available online: http://wwww.tandfonline.com/10.1198/jasa.2009.tm08024.

Keywords

basis expansion, functional data analysis, penalization, regularization, spatial-temporal modeling

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Date Posted: 27 November 2017