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A divisive clustering method for functional data with special consideration of outliers

Author

Listed:
  • Ana Justel

    (Universidad Autònoma de Madrid
    Universidad Carlos III de Madrid)

  • Marcela Svarc

    (Universidad de San Andrés
    CONICET)

Abstract

This paper presents DivClusFD, a new divisive hierarchical method for the non-supervised classification of functional data. Data of this type present the peculiarity that the differences among clusters may be caused by changes as well in level as in shape. Different clusters can be separated in different subregion and there may be no subregion in which all clusters are separated. In each step of division, the DivClusFD method explores the functions and their derivatives at several fixed points, seeking the subregion in which the highest number of clusters can be separated. The number of clusters is estimated via the gap statistic. The functions are assigned to the new clusters by combining the k-means algorithm with the use of functional boxplots to identify functions that have been incorrectly classified because of their atypical local behavior. The DivClusFD method provides the number of clusters, the classification of the observed functions into the clusters and guidelines that may be for interpreting the clusters. A simulation study using synthetic data and tests of the performance of the DivClusFD method on real data sets indicate that this method is able to classify functions accurately.

Suggested Citation

  • Ana Justel & Marcela Svarc, 2018. "A divisive clustering method for functional data with special consideration of outliers," 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. 12(3), pages 637-656, September.
    • Handle: RePEc:spr:advdac:v:12:y:2018:i:3:d:10.1007_s11634-017-0290-1
    DOI: 10.1007/s11634-017-0290-1
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    References listed on IDEAS

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    1. 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.
    2. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    3. Sara López-Pintado & Ying Sun & Juan Lin & Marc Genton, 2014. "Simplicial band depth for multivariate functional data," 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. 8(3), pages 321-338, September.
    4. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    5. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    6. Francesca Ieva & Anna M. Paganoni & Davide Pigoli & Valeria Vitelli, 2013. "Multivariate functional clustering for the morphological analysis of electrocardiograph curves," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(3), pages 401-418, May.
    7. Shuichi Tokushige & Hiroshi Yadohisa & Koichi Inada, 2007. "Crisp and fuzzy k-means clustering algorithms for multivariate functional data," Computational Statistics, Springer, vol. 22(1), pages 1-16, April.
    8. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    9. C. Abraham & P. A. Cornillon & E. Matzner‐Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B‐Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595, September.
    10. Fraiman, Ricardo & Justel, Ana & Svarc, Marcela, 2008. "Selection of Variables for Cluster Analysis and Classification Rules," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1294-1303.
    11. Charles Bouveyron & Julien Jacques, 2011. "Model-based clustering of time series in group-specific functional subspaces," 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 281-300, December.
    12. Shubhankar Ray & Bani Mallick, 2006. "Functional clustering by Bayesian wavelet methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 305-332, April.
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