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Benchmarking different clustering algorithms on functional data

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  • Christina Yassouridis

    (University of Natural Resources and Life Sciences, Institute of Applied Statistics and Computing)

  • Friedrich Leisch

    (University of Natural Resources and Life Sciences, Institute of Applied Statistics and Computing)

Abstract

Theoretical knowledge of clustering functions is still scarce and only few models are available in form of applicable code. In literature, most methods are based on the projection of the functions onto a basis and building fixed or random effects models of the basis coefficients. They involve various parameters, among them number of basis functions, projection dimension, number of iterations etc. They usually work well on the data presented in the articles, but their performance has in most cases not been tested objectively on other data sets, nor against each other. The purpose of this paper is to give an overview of several existing methods to cluster functional data. An outline of their theoretic concepts is given and the meaning of their hyperparameters is explained. A simulation study was set up to analyze the parameters’ efficiency and sensitivity on different types of data sets, that were registered on regular and on irregular grids. For each method, a linear model of the clustering results was evaluated with different parameter levels as predictors. Later, the methods’ performances were compared to each other with the help of a visualization tool, to identify which method works the best on a specific kind of data.

Suggested Citation

  • Christina Yassouridis & Friedrich Leisch, 2017. "Benchmarking different clustering algorithms on 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. 11(3), pages 467-492, September.
    • Handle: RePEc:spr:advdac:v:11:y:2017:i:3:d:10.1007_s11634-016-0261-y
    DOI: 10.1007/s11634-016-0261-y
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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, September.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
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    Cited by:

    1. Pedro C. Álvarez-Esteban & Luis A. García-Escudero, 2022. "Robust clustering of functional directional 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. 16(1), pages 181-199, March.

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