title: Interpretable functional principal component analysis.
abstract: Functional principal component analysis (FPCA) is a popular approach to explore major sources of variation in a sample of random curves. These major sources of variation are represented by functional principal components (FPCs). The intervals where the values of FPCs are significant are interpreted as where sample curves have major variations. However, these intervals are often hard for naïve users to identify, because of the vague definition of "significant values". In this article, we develop a novel penalty-based method to derive FPCs that are only nonzero precisely in the intervals where the values of FPCs are significant, whence the derived FPCs possess better interpretability than the FPCs derived from existing methods. To compute the proposed FPCs, we devise an efficient algorithm based on projection deflation techniques. We show that the proposed interpretable FPCs are strongly consistent and asymptotically normal under mild conditions. Simulation studies confirm that with a competitive performance in explaining variations of sample curves, the proposed FPCs are more interpretable than the traditional counterparts. This advantage is demonstrated by analyzing two real datasets, namely, electroencephalography data and Canadian weather data.
authors.affiliation: Department of Statistical Sciences, University of Toronto, Toronto, Ontario, M5S 3G3, Canada. zhenhua@utstat.toronto.edu.
authors.forename: Zhenhua
authors.initials: Z
authors.lastname: Lin
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada. lwa68@sfu.ca.
authors.forename: Liangliang
authors.initials: L
authors.lastname: Wang
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada. jca76@sfu.ca.
authors.forename: Jiguo
authors.initials: J
authors.lastname: Cao
mesh_terms: D000465:Algorithms; D002170:Canada; D003198:Computer Simulation; D004569:Electroencephalography / Q000706:statistics & numerical data; D006801:Humans; D015233:Models, Statistical; D025341:Principal Component Analysis / Q000379:methods*; D014887:Weather
keywords: EEG; Functional data analysis; Null region; Penalized B-spline; Projection deflation; Regularization; Sparse PCA