Jeng-Min ChiouPai-Ling Li2024-09-032024-09-032007-08-02https://scholars.lib.ntu.edu.tw/handle/123456789/720681A 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.ClassificationClusteringFunctional dataFunctional principal component analysisModes of variationStochastic processesjournal article10.1111/j.1467-9868.2007.00605.x