Clustering of functional data in a low-dimensional subspace
To find optimal clusters of functional objects in a lower-dimensional subspace of data, a sequential method called tandem analysis, is often used, though such a method is problematic. A new procedure is developed to find optimal clusters of functional objects and also find an optimal subspace for clustering, simultaneously. The method is based on the k-means criterion for functional data and seeks the subspace that is maximally informative about the clustering structure in the data. An efficient alternating least-squares algorithm is described, and the proposed method is extended to a regularized method. Analyses of artificial and real data examples demonstrate that the proposed method gives correct and interpretable results. Copyright Springer-Verlag 2012
Volume (Year): 6 (2012)
Issue (Month): 3 (October)
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- C. Abraham & P. A. Cornillon & E. Matzner-Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B-Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595.
- Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
- Philippe Besse & J. Ramsay, 1986. "Principal components analysis of sampled functions," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 285-311, June.
- Hardy, Andre, 1996. "On the number of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 83-96, November.
- Timmerman, Marieke E. & Ceulemans, Eva & Kiers, Henk A.L. & Vichi, Maurizio, 2010. "Factorial and reduced K-means reconsidered," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1858-1871, July.
- Tarpey, Thaddeus, 2007. "Linear Transformations and the k-Means Clustering Algorithm: Applications to Clustering Curves," The American Statistician, American Statistical Association, vol. 61, pages 34-40, February.
- Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
- Charles Bouveyron & Julien Jacques, 2011. "Model-based clustering of time series in group-specific functional subspaces," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 281-300, December.
- Douglas Steinley & Robert Henson, 2005. "OCLUS: An Analytic Method for Generating Clusters with Known Overlap," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 221-250, September.
- Vichi, Maurizio & Kiers, Henk A. L., 2001. "Factorial k-means analysis for two-way data," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 49-64, July.
- Besse, Philippe C. & Cardot, Herve & Ferraty, Frederic, 1997. "Simultaneous non-parametric regressions of unbalanced longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 255-270, May.
- Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 159-179, June.
- Jan Leeuw & Forrest Young & Yoshio Takane, 1976. "Additive structure in qualitative data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 471-503, December.
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