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Functional clustering and identifying substructures of longitudinal data
Author(s) -
Chiou JengMin,
Li PaiLing
Publication year - 2007
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00605.x
Subject(s) - cluster analysis , identifiability , covariance , cluster (spacecraft) , data mining , functional principal component analysis , parametric statistics , functional data analysis , mathematics , hierarchical clustering , computer science , algorithm , statistics , programming language
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, the k ‐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.