Functional clustering and identifying substructures of longitudinal data

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 69, Issue 4, 2007, Pages 679-699

  Chiou, Jeng Min ^a,c   Li, Pai Ling ^b  

^a ACADEMIA SINICA   (Taiwan)

^b TAMKANG UNIVERSITY   (Taiwan)

^c INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Classification; Clustering; Functional data; Functional principal component analysis; Modes of variation; Stochastic processes

Indexed keywords

EID: 34547837451     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2007.00605.x     Document Type: Article

References (33)

1. Abraham, C., Cornillon, P. A., Matzner-Løber, E. Molinari, N. (2003) Unsupervised curve clustering using B-splines. Scand. J. Statist., 30, 581 595.
2. Arbeitman, M. N., Furlong, E. E. M., Imam, F., Johnson, E., Null, B. H., Baker, B. S., Krasnow, M. A., Scott, M. P., Davis, R. W. White, K. P. (2002) Gene expression during the life cycle of Drosophila melanogaster. Science, 297, 2270 2275.
3. Ash, R. B. (1972) Real Analysis and Probability. London : Academic Press.
4. Ash, R. B. Gardner, M. F. (1975) Topics in Stochastic Processes. New York : Academic Press.
5. Ball, G. H. Hall, D. J. (1967) A clustering technique for summarizing multivariate data. Behav. Sci., 12, 153 155.
6. Bock, H. H. (1987) On the interface between cluster analysis, principal component analysis, and multidimensional scaling. In Multivariate Statistical Modeling and Data Analysis (eds H. Bozdogan A. K. Gupta pp. 17 44. Dordrecht : Reidel.
7. Chiou, J.-M., Müller, H.-G. Wang, J.-L. (2003) Functional quasi-likelihood regression model with smooth random effects. J. R. Statist. Soc. B, 65, 405 423.
8. Fan, J. Gijbels, I. (1996) Local Polynomial Modelling and Its Application. London : Chapman and Hall.
9. Fraley, C. Raftery, A. E. (2002) Model-based clustering, discriminant analysis and density estimation. J. Am. Statist. Ass., 97, 611 631.
10. García-Escudero, L. A. Gordaliza, A. (2005) A proposal for robust curve clustering. J. Classificn, 22, 185 201.
11. Hall, P., Müller, H. G. Wang, J. L. (2006) Properties of principal component methods for functional and longitudinal data analysis. Ann. Statist., 34, 1493 1517.
12. Heckman, N. E. Zamar, R. H. (2000) Comparing the shapes of regression functions. Biometrika, 87, 135 144.
13. Hubert, L. Arabie, P. (1985) Comparing partitions. J. Classificn, 2, 193 218.
14. Jain, A. K. Dubes, R. C. (1988) Algorithms for Clustering Data. Englewood Cliffs : Prentice Hall.
15. James, G. M. Sugar, C. A. (2003) Clustering for sparsely sampled functional data. J. Am. Statist. Ass., 98, 397 408.
16. Jolliffe, I. T. (2002) Principal Component Analysis. New York : Springer.
17. Leng, X. Müller, H. G. (2006) Classification using functional data analysis for temporal gene expression data. Bioinformatics, 22, 68 76.
18. Li, J. (2005) Clustering based on multilayer mixture models. J. Comput. Graph. Statist., 14, 547 568.
19. Liu, X. Müller, H. G. (2003) Modes and clustering for time-warped gene expression profile data. Bioinformatics, 19, 1937 1944.
20. Luan, Y. Li, H. (2003) Clustering of time-course gene expression data using a mixed-effects model with B-splines. Bioinformatics, 19, 474 482.
21. MacQueen, J. B 1967) Some methods for classification and analysis of multivariate observations. In Proc. 5th Berkeley Symp. Mathematical Statistics and Probability, vol. 1, pp. 281 297. Berkeley : University of California Press.
22. Pollard, D. (1981) Strong consistency of k-means clustering. Ann. Statist., 9, 135 140.
23. Rand, W. M. (1971) Objective criteria for the evaluation of clustering methods. J. Am. Statist. Ass., 66, 846 850.
24. Ray, S. Mallick, B. (2006) Functional clustering by Bayesian wavelet methods. J. R. Statist. Soc. B, 68, 305 332.
25. Serban, N. Wasserman, L. (2005) CATS: clustering after transformation and smoothing. J. Am. Statist. Ass., 100, 990 999.
26. Tarpey, T. Kinateder, K. K. J. (2003) Clustering functional data. J. Classificn, 20, 93 114.
27. Tuddenham, R. D. Snyder, M. M. (1954) Physical growth of California boys and girls from birth to eighteen years. Univ. Calif. Publ. Chld Devlpmnt, 1, 183 364.
28. Ward, J. H. (1963) Hierarchical groupings to optimize an objective function. J. Am. Statist. Ass., 58, 236 244.
29. Westfall, P. H. Young, S. S. (1993) Resampling-based Multiple Testing: Examples and Methods for p-value Adjustment. New York : Wiley.
30. Yao, F., Müller, H. G., Clifford, A. J., Dueker, S. R., Follett, J., Lin, Y., Buchholz, B. A. Vogel, J. S. (2003) Shrinkage estimation for functional principal component scores, with application to the population kinetics of plasma folate. Biometrics, 59, 676 685.
31. Yao, F., Müller, H. G. Wang, J. L. (2005) Functional data analysis for sparse longitudinal data. J. Am. Statist. Ass., 100, 577 590.
32. Yeung, K. Y., Fraley, C., Muruan, A., Raftery, A. E. Ruzzo, W. L. (2001) Model-based clustering and data transformation for gene expression data. Bioinformatics, 17, 977 987.
33. Yeung, K. Y. Ruzzo, W. L. (2001) Principal component analysis for clustering gene expression data. Bioinformatics, 17, 763 774.