Functional Clustering and Identifying Substructures of Longitudinal Data

Abstract

Summary.A functional clustering (FC) method, k-centres FC, for longitudinal data is proposed. The k-centres FC approach accounts for both the means and the modes of variation differentials between clusters by predicting cluster membership with a reclassification step.The cluster membership predictions are based on a non-parametric random-effect model of the truncated Karhunen-Loève expansion, coupled with a non-parametric iterative mean and covariance updating scheme. We show that, under the identifiability conditions derived, the k-centres FC method proposed can greatly improve cluster quality as compared with conventional clustering algorithms. Moreover, by exploring the mean and covariance functions of each cluster, the k-centres FC method provides an additional insight into cluster structures which facilitates functional cluster analysis. Practical performance of the k-centres FC method is demonstrated through simulation studies and data applications including growth curve and gene expression profile data.

Robust functional clustering of ERP data with application to a study of implicit learning in autism

“…Our work builds on the FC algorithm proposed by Chiou and Li (2007). The original formulation of FC assumes identical mean and covariance cluster membership.…”

“…Section 3 provides background on FPCA and introduces the proposed RFC algorithm for single-and multilevel functional data. Section 4 applies the proposed RFC to the autism study and compares the results with those obtained from alternative algorithms including FC of Chiou and Li (2007). We study the performance of the proposed algorithm in extensive simulations summarized in Section 5 and conclude with a brief discussion (Section 6).…”

A survey of functional principal component analysis

“…Later, Grenander (1950) Due to the theoretical and practical developments, FPCA has been successfully applied to many practical problems, such as the analysis of cornea curvature in the human eye (Locantore et al 1999), the analysis of electronic commerce , the analysis of growth curve (Chiou & Li 2007), the analysis of income density curves (Kneip & Utikal 2001), the analysis of implied volatility surface in finance (Cont & de Fonseca 2002), the analysis of longitudinal primary biliary liver cirrhosis (Yao et al 2005b), the analysis of spectroscopy data (Yao & Müller 2010), signal discrimination (Hall et al 2001), and time-course gene expression (Yao et al 2005a). Furthermore, Hyndman & Ullah (2007) proposed a smoothed and robust FPCA, and used it to forecast age-specific mortality and fertility rates.…”

Classification of nonparametric regression functions in heterogeneous panels

“…, X n into a number of groups. There is a vast amount of papers which deal with this problem in different model setups; see for example Abraham et al (2003) and Tarpey and Kinateder (2003) for procedures based on k-means clustering, James and Sugar (2003) and Chiou and Li (2007) for so-called model-based clustering approaches, Ray and Mallick (2006) for a Bayesian approach and Jacques and Preda (2014) for a recent survey.…”