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Outlier detection in multivariate functional data through a contaminated mixture model

Author

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  • Amovin-Assagba, Martial
  • Gannaz, Irène
  • Jacques, Julien

Abstract

In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as the detection of outliers in a multivariate functional data set. Due to the heterogeneity of this data set, the proposed contaminated mixture model both clusters the multivariate functional data into homogeneous groups and detects outliers. The main advantage of this procedure over its competitors is that it does not require to specify the proportion of outliers. Model inference is performed through an Expectation-Conditional Maximization algorithm, and the BIC is used to select the number of clusters. Numerical experiments on simulated data demonstrate the high performance achieved by the inference algorithm. In particular, the proposed model outperforms the competitors. Its application on the real data which motivated this study allows to correctly detect abnormal behaviors.

Suggested Citation

  • Amovin-Assagba, Martial & Gannaz, Irène & Jacques, Julien, 2022. "Outlier detection in multivariate functional data through a contaminated mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:csdana:v:174:y:2022:i:c:s0167947322000767
    DOI: 10.1016/j.csda.2022.107496
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    References listed on IDEAS

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    1. Di Zio, Marco & Guarnera, Ugo & Rocci, Roberto, 2007. "A mixture of mixture models for a classification problem: The unity measure error," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2573-2585, February.
    2. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    3. Antonio Punzo & Angelo Mazza & Antonello Maruotti, 2018. "Fitting insurance and economic data with outliers: a flexible approach based on finite mixtures of contaminated gamma distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(14), pages 2563-2584, October.
    4. Anastasios Bellas & Charles Bouveyron & Marie Cottrell & Jérôme Lacaille, 2013. "Model-based clustering of high-dimensional data streams with online mixture of probabilistic PCA," 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. 7(3), pages 281-300, September.
    5. 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.
    6. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    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. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," 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 231-255, September.
    9. Giorgino, Toni, 2009. "Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i07).
    10. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    11. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
    12. Salvatore D. Tomarchio & Antonio Punzo, 2020. "Dichotomous unimodal compound models: application to the distribution of insurance losses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2328-2353, November.
    13. 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.
    14. Heard, Nicholas A. & Holmes, Christopher C. & Stephens, David A., 2006. "A Quantitative Study of Gene Regulation Involved in the Immune Response of Anopheline Mosquitoes: An Application of Bayesian Hierarchical Clustering of Curves," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 18-29, March.
    15. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    16. Antonio Punzo, 2019. "A new look at the inverse Gaussian distribution with applications to insurance and economic data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(7), pages 1260-1287, May.
    17. 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.
    18. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Rejoinder to ‘multivariate functional outlier detection’," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 269-277, July.
    19. Dai, Wenlin & Genton, Marc G., 2019. "Directional outlyingness for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 50-65.
    20. Amandine Schmutz & Julien Jacques & Charles Bouveyron & Laurence Chèze & Pauline Martin, 2020. "Clustering multivariate functional data in group-specific functional subspaces," Computational Statistics, Springer, vol. 35(3), pages 1101-1131, September.
    21. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2017. "Multivariate and functional classification using depth and distance," 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 445-466, September.
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