The Analysis of Two-Way Functional Data Using Two-Way Regularized Singular Value Decompositions

• 成果类型: Article
• 署名作者: Huang, Jianhua Z.; Shen, Haipeng; Buja, Andreas
• 署名单位: Texas A&M University System; Texas A&M University College Station; University of North Carolina; University of North Carolina Chapel Hill; University of Pennsylvania
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.tm08024
• 发表日期: 2009
• 页码: 1609-1620
• 关键词: canonical correlation-analysis; CURVES; mortality; models

摘要

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 oil 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.