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A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data

Author

Listed:
  • Andrea Martino

    (Politecnico di Milano)

  • Andrea Ghiglietti

    (Livanova)

  • Francesca Ieva

    (Politecnico di Milano)

  • Anna Maria Paganoni

    (Politecnico di Milano)

Abstract

This paper proposes a clustering procedure for samples of multivariate functions in $$(L^2(I))^{J}$$ ( L 2 ( I ) ) J , with $$J\ge 1$$ J ≥ 1 . This method is based on a k-means algorithm in which the distance between the curves is measured with a metric that generalizes the Mahalanobis distance in Hilbert spaces, considering the correlation and the variability along all the components of the functional data. The proposed procedure has been studied in simulation and compared with the k-means based on other distances typically adopted for clustering multivariate functional data. In these simulations, it is shown that the k-means algorithm with the generalized Mahalanobis distance provides the best clustering performances, both in terms of mean and standard deviation of the number of misclassified curves. Finally, the proposed method has been applied to two case studies, concerning ECG signals and growth curves, where the results obtained in simulation are confirmed and strengthened.

Suggested Citation

  • Andrea Martino & Andrea Ghiglietti & Francesca Ieva & Anna Maria Paganoni, 2019. "A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 301-322, June.
    • Handle: RePEc:spr:stmapp:v:28:y:2019:i:2:d:10.1007_s10260-018-00446-6
    DOI: 10.1007/s10260-018-00446-6
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    References listed on IDEAS

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    1. 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.
    2. repec:cte:wsrepe:ws131312 is not listed on IDEAS
    3. Boudaoud, S. & Rix, H. & Meste, O., 2010. "Core Shape modelling of a set of curves," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 308-325, February.
    4. 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.
    5. 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.
    6. Ghiglietti, Andrea & Paganoni, Anna Maria, 2017. "Exact tests for the means of Gaussian stochastic processes," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 102-107.
    7. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    8. Melnykov, Igor & Melnykov, Volodymyr, 2014. "On K-means algorithm with the use of Mahalanobis distances," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 88-95.
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    Cited by:

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    3. Daewon Yang & Taeryon Choi & Eric Lavigne & Yeonseung Chung, 2022. "Non‐parametric Bayesian covariate‐dependent multivariate functional clustering: An application to time‐series data for multiple air pollutants," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1521-1542, November.

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