Identifying cluster number for subspace projected functional data clustering
We propose a new approach, the forward functional testing (FFT) procedure, to cluster number selection for functional data clustering. We present a framework of subspace projected functional data clustering based on the functional multiplicative random-effects model, and propose to perform functional hypothesis tests on equivalence of cluster structures to identify the number of clusters. The aim is to find the maximum number of distinctive clusters while retaining significant differences between cluster structures. The null hypotheses comprise equalities between the cluster mean functions and between the sets of cluster eigenfunctions of the covariance kernels. Bootstrap resampling methods are developed to construct reference distributions of the derived test statistics. We compare several other cluster number selection criteria, extended from methods of multivariate data, with the proposed FFT procedure. The performance of the proposed approaches is examined by simulation studies, with applications to clustering gene expression profiles.
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- Sugar, Catherine A. & James, Gareth M., 2003. "Finding the Number of Clusters in a Dataset: An Information-Theoretic Approach," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 750-763, January.
- Luis Angel Garcia-Escudero & Alfonso Gordaliza, 2005. "A Proposal for Robust Curve Clustering," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 185-201, September.
- Zeng, Yujing & Garcia-Frias, Javier, 2006. "A novel HMM-based clustering algorithm for the analysis of gene expression time-course data," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2472-2494, May.
- Shubhankar Ray & Bani Mallick, 2006. "Functional clustering by Bayesian wavelet methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 305-332.
- Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
- Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
- 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.
- Jeng-Min Chiou & Pai-Ling Li, 2007. "Functional clustering and identifying substructures of longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 679-699.
- Serban, Nicoleta & Wasserman, Larry, 2005. "CATS: Clustering After Transformation and Smoothing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 990-999, September.
- Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Vitelli, Valeria, 2010. "k-mean alignment for curve clustering," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1219-1233, May.
- Ma, Ping & Zhong, Wenxuan, 2008. "Penalized Clustering of Large-Scale Functional Data With Multiple Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 625-636, June.
- Liu, Xueli & Yang, Mark C.K., 2009. "Simultaneous curve registration and clustering for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1361-1376, February.
- 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.
- James G.M. & Sugar C.A., 2003. "Clustering for Sparsely Sampled Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 397-408, January.
- Chiou, Jeng-Min & Li, Pai-Ling, 2008. "Correlation-Based Functional Clustering via Subspace Projection," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1684-1692.
- Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
- 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.
- Hardy, Andre, 1996. "On the number of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 83-96, November.
- Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
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