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.