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Simultaneous curve registration and clustering for functional data

Author

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  • Liu, Xueli
  • Yang, Mark C.K.

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1361-1376
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    References listed on IDEAS

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    1. 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.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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. 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.
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    Citations

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    Cited by:

    1. Maire, Florian & Moulines, Eric & Lefebvre, Sidonie, 2017. "Online EM for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 27-47.
    2. Wu, Zizhen & Hitchcock, David B., 2016. "A Bayesian method for simultaneous registration and clustering of functional observations," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 121-136.
    3. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    4. Allou Samé & Faicel Chamroukhi & Gérard Govaert & Patrice Aknin, 2011. "Model-based clustering and segmentation of time series with changes in regime," 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 301-321, December.
    5. Faicel Chamroukhi, 2016. "Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 374-411, October.
    6. 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.
    7. repec:bla:biomet:v:73:y:2017:i:1:p:324-333 is not listed on IDEAS
    8. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    9. Slaets, Leen & Claeskens, Gerda & Hubert, Mia, 2012. "Phase and amplitude-based clustering for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2360-2374.

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