Simultaneous curve registration and clustering for functional data

Computational Statistics and Data Analysis

Volumn 53, Issue 4, 2009, Pages 1361-1376

  Liu, Xueli ^a   Yang, Mark C K ^a  

^a University of Florida ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LEARNING SYSTEMS;

DYNAMIC PROCESSES; GROWTH CURVES; PHASE VARIATIONS; SIMULATION STUDIES; TIME-SPACE; TYPE LEARNING;

LEARNING ALGORITHMS;

EID: 58549098884     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2008.11.019     Document Type: Article

References (38)

1. Brumback L.C., and Lindstrom M.J. Self modelling with flexible, random time transformations. Biometrics 60 (2004) 461-470
2. Chiou J.M., and Li P.L. Functional clustering and identifying substructures of longitudinal data. J. Roy. Statist. Soc. Ser. B 69 (2007) 679-699
3. Chou W., and Reichl W. Decision tree state typing based on penalized Bayesian information criterion. Proc. IEEE Int. Conf. Acoust., Speech, Signal Process (1999) 345-348
4. De Boor C. A Practical Guide to Splines (1978), Springer-Verlag
5. Fraley C., and Raftery A.E. Model-based clustering, discriminant analysis, and density estimation. J. Amer. Statist. Assoc. 97 (2002) 611-631
6. Gaffney, S., 2004. Probabilistic curve-aligned clustering and prediction with mixture models. Ph.D. Dissertation. Department of Computer Science, University of California, Irvine
7. Gaffney S., and Smyth P. Joint probabilistic curve clustering and alignment. Advances in Neural Information Processing Systems (2004), NY: MIT Press
8. García-Escudero L.A., and Gordaliza A. A proposal for robust curve clustering. J. Classification 22 (2005) 185-201
9. Gasser Th., and Kneip A. Searching for structure in curve samples. J. Amer. Statist. Assoc. 90 (1995) 1179-1188
10. Gasser Th., Köhler W., Müller H.G., Kneip A., Largo R., Molinari L., and Prader A. Velocity and acceleration of height growth using kernel estimation. Ann. Human Biol. 11 (1984) 397-411
11. Gasser Th., Müller H.G., Köhler W., Molinari L., and Prader A. Nonparametric regression analysis of growth curves. Ann. Statist. 12 (1984) 210-229
12. Gervini D., and Gasser Th. Self-modelling warping functions. J. Roy. Statist. Soc. Ser. B 66 (2004) 959-971
13. Gervini D., and Gasser Th. Nonparametric maximum likelihood estimation of the structural mean of a sample of curves. Biometrika 92 (2005) 801-820
14. Hubert L., and Arabie P. Comparing partitions. J. Classification 2 (1985) 193-218
15. James G., and Sugar C.A. Clustering for sparsely sampled functional data. J. Amer. Statist. Assoc. 98 (2003) 397-408
16. Kneip A., and Gasser Th. Convergence and consistency results for self-modelling regression. Ann. Statist. 16 (1988) 82-112
17. Kneip A., and Gasser Th. Statistical tools to analyze data representing a sample of curves. Ann. Statist. 20 (1992) 1266-1305
18. Kneip A., Li X., MacGibbon K.B., and Ramsay J.O. Curve registration by local regression. Canad. J. Statist. 28 (2000) 19-29
19. Lindstrom M.J., and Bates D.M. Nonlinear mixed effects models for repeated measures data. Biometrics 46 (1990) 673-687
20. Liu X., and Müller H.G. Modes and clustering for time-warped gene expression profile data. Bioinformatics 19 (2003) 1937-1944
21. Liu X., and Müller H.G. Functional convex averaging and synchronization for time-warped random curves. J. Amer. Statist. Assoc. 99 (2004) 687-699
22. Luan Y., and Li H. Clustering of time-course gene expression data using a mixed-effects model with B-splines. Bioinformatics 19 (2003) 474-482
23. Patterson T.N.L. The optimum addition of points to quadrature formulae. Math. Comput. 22 (1968) 847-856
24. Ramsay J.O., and Li X. Curve registration. J. Roy. Statist. Soc. Ser. B 60 (1998) 351-363
25. Ramsay J.O., and Silverman B. Functional Data Analysis (1997), Springer, New York
26. Ramsay J.O., and Silverman B. Applied Functional Data Analysis: Methods and Case Studies (2002), Springer, New York
27. Rand W.M. Objective criteria for the evaluation of clustering methods. J. Amer. Statist. Assoc. 66 (1971) 846-850
28. Rønn B.B. Nonparametric maximum likelihood estimation for shifted curves. J. Roy. Statist. Soc. Ser. B 63 (2001) 243-259
29. Sakoe H., and Chiba S. Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. Acoustics Speech Signal Process. 26 (1978) 43-49
30. Serban N., and Wasserman L. CATS: Clustering after transformation and smoothing. J. Amer. Statist. Assoc. 100 (2005) 990-999
31. Shibata R. An optimal selection of regression variables. Biometrika 68 (1981) 45-54
32. Tarpey T. Linear transformations and the k-Means clustering algorithm: Applications to clustering curves. Amer. Statist. 61 (2007) 34-40
33. Tarpey T., and Kinateder K.J. Clustering functional data. J. Classification 20 (2003) 93-114
34. Verbeke G., and Molenberghs G. Linear Mixed Models for Longitudinal Data (2000), Springer, New York
35. Wang K., and Gasser Th. Alignment of curves by dynamic time warping. Ann. Statist. 25 (1997) 1251-1276
36. Wang K., and Gasser Th. Asymptotic and bootstrap confidence bounds for the structural average of curves. Ann. Statist. 26 (1998) 972-991
37. Wang K., and Gasser Th. Synchronizing sample curves nonparametrically. Ann. Statist. 27 (1999) 439-460
38. Wolfinger R. Laplace's approximation for nonlinear mixed models. Biometrika 80 (1993) 791-795