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Simultaneous curve registration and clustering for functional data

  • Liu, Xueli
  • Yang, Mark C.K.
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    Study of dynamic processes in many areas of science has led to the appearance of functional data sets. It is often the case that individual trajectories vary both in the amplitude space and in the time space. We develop a coherent clustering procedure that allows for temporal aligning. Under this framework, closed form solutions of an EM type learning algorithm are derived. The method can be applied to all types of curve data but is particularly useful when phase variation is present. We demonstrate the method by both simulation studies and an application to human growth curves.

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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 53 (2009)
    Issue (Month): 4 (February)
    Pages: 1361-1376

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    Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1361-1376
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer, vol. 2(1), pages 193-218, December.
    2. Birgitte B. Rønn, 2001. "Nonparametric maximum likelihood estimation for shifted curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 243-259.
    3. 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.
    4. Xueli Liu & Hans-Georg Muller, 2004. "Functional Convex Averaging and Synchronization for Time-Warped Random Curves," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 687-699, January.
    5. Daniel Gervini & Theo Gasser, 2005. "Nonparametric maximum likelihood estimation of the structural mean of a sample of curves," Biometrika, Biometrika Trust, vol. 92(4), pages 801-820, December.
    6. Luis Angel Garcia-Escudero & Alfonso Gordaliza, 2005. "A Proposal for Robust Curve Clustering," Journal of Classification, Springer, vol. 22(2), pages 185-201, September.
    7. 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.
    8. 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.
    9. Daniel Gervini & Theo Gasser, 2004. "Self-modelling warping functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 959-971.
    10. Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
    11. 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.
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