Functional Clustering and Identifying Substructures of Longitudinal Data

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, 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.