Autocorrelation-based fuzzy clustering of time series
Fuzzy Sets and Systems
Kml: A package to cluster longitudinal data
Computer Methods and Programs in Biomedicine
Wavelets-based clustering of multivariate time series
Fuzzy Sets and Systems
Functional fuzzy clusterwise regression analysis
Advances in Data Analysis and Classification
Model-based clustering for multivariate functional data
Computational Statistics & Data Analysis
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Functional data analysis, as proposed by Ramsay (Psychometrika 47:379---396, 1982), has recently attracted many researchers. The most popular approach taken in recent studies of functional data has been the extension of statistical methods for the analysis of usual data to that of functional data (e.g., Ramsay and Silverman in Functional data Analysis Springer, Berlin Heidelberg New York, 1997, Applied functional data analysis: methods and case studies. Springer, Berlin Heidelberg New York, 2002; Mizuta in Proceedings of the tenth Japan and Korea Joint Conference of Statistics, pp 77---82, 2000; Shimokawa et al. in Japan J Appl Stat 29:27---39, 2000). In addition, several methods for clustering functional data have been proposed (Abraham et al. in Scand J Stat 30:581---595, 2003; Gareth and Catherine in J Am Stat Assoc 98:397---408, 2003; Tarpey and kinateder in J Classif 20:93---114, 2003; Rossi et al. in Proceedings of European Symposium on Artificial Neural Networks pp 305---312, 2004). Furthermore, Tokushige et al. (J Jpn Soc Comput Stat 15:319---326, 2002) defined several dissimilarities between functions for the case of functional data. In this paper, we extend existing crisp and fuzzy k-means clustering algorithms to the analysis of multivariate functional data. In particular, we consider the dissimilarity between functions as a function. Furthermore, cluster centers and memberships, which are defined as functions, are determined at the minimum of a certain target function by using a calculus-of-variations approach.