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Functional clustering and identifying substructures of longitudinal data

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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–Lo√®ve 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.
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Keywords: Classification; Clustering; Functional data; Functional principal component analysis; Modes of variation; Stochastic processes

Document Type: Research Article

Affiliations: 1: Academia Sinica, Taipei, Taiwan 2: Tamkang University, Taiwan

Publication date: 2007-09-01

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