Functional Clustering and Identifying Substructures of Longitudinal Data
Journal
Journal of the Royal Statistical Society Series B: Statistical Methodology
Journal Volume
69
Journal Issue
4
Start Page
679-699
ISSN
1369-7412
1467-9868
Date Issued
2007-08-02
Author(s)
Pai-Ling Li
Abstract
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, thek-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. © 2007 Royal Statistical Society.
Subjects
Classification
Clustering
Functional data
Functional principal component analysis
Modes of variation
Stochastic processes
Publisher
Oxford University Press (OUP)
Type
journal article