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Functional clustering and identifying substructures of longitudinal data

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  • Jeng-Min Chiou
  • Pai-Ling Li
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    Abstract

    A functional clustering (FC) method, "k"-centres FC, for longitudinal data is proposed. The "k"-centres FC approach accounts for both the means and the modes of variation differentials between clusters by predicting cluster membership with a reclassification step. The cluster membership predictions are based on a non-parametric random-effect model of the truncated Karhunen-Loève expansion, coupled with a non-parametric iterative mean and covariance updating scheme. We show that, under the identifiability conditions derived, the "k"-centres FC method proposed can greatly improve cluster quality as compared with conventional clustering algorithms. Moreover, by exploring the mean and covariance functions of each cluster, the"k"-centres FC method provides an additional insight into cluster structures which facilitates functional cluster analysis. Practical performance of the "k"-centres FC method is demonstrated through simulation studies and data applications including growth curve and gene expression profile data. Copyright 2007 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 69 (2007)
    Issue (Month): 4 ()
    Pages: 679-699

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    Handle: RePEc:bla:jorssb:v:69:y:2007:i:4:p:679-699

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    Cited by:
    1. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    2. Poskitt, D.S. & Sengarapillai, Arivalzahan, 2013. "Description length and dimensionality reduction in functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 98-113.
    3. Alonso, Andrés M. & Casado, David & Romo, Juan, 2012. "Supervised classification for functional data: A weighted distance approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2334-2346.
    4. Haeran Cho & Yannig Goude & Xavier Brossat & Qiwei Yao, 2013. "Modeling and forecasting daily electricity load curves: a hybrid approach," LSE Research Online Documents on Economics 49634, London School of Economics and Political Science, LSE Library.
    5. 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.
    6. 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.
    7. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2014. "Functional k-means inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 172-182.
    8. 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.
    9. 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, vol. 5(4), pages 301-321, December.

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