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A Kemeny Distance-Based Robust Fuzzy Clustering for Preference Data

Author

Listed:
  • Pierpaolo D’Urso

    (Sapienza University of Rome)

  • Vincenzina Vitale

    (Sapienza University of Rome)

Abstract

We propose two robust fuzzy clustering techniques in the context of preference rankings to group judges into homogeneous clusters even in the case of contamination due to outliers or, more generally, noisy data. The two fuzzy C-Medoids clustering methods, based on the same suitable exponential transformation of the Kemeny distance, belong to two different approaches and differ in the way they introduce the fuzziness in the membership matrix, the one based on the “m” exponent and the other on the Shannon entropy. As far as the Kemeny distance is concerned, it is equivalent to the Kendall distance in the case of complete rankings but differs from the latter in the way of handling tied rankings. Simulations prove that our methods are able to recover the natural structure of the groups neutralizing the effect of possible noises and outliers. Two applications to real datasets are also provided.

Suggested Citation

  • Pierpaolo D’Urso & Vincenzina Vitale, 2022. "A Kemeny Distance-Based Robust Fuzzy Clustering for Preference Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 600-647, November.
    • Handle: RePEc:spr:jclass:v:39:y:2022:i:3:d:10.1007_s00357-022-09420-0
    DOI: 10.1007/s00357-022-09420-0
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    References listed on IDEAS

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    1. Coppi, Renato & D'Urso, Pierpaolo, 2006. "Fuzzy unsupervised classification of multivariate time trajectories with the Shannon entropy regularization," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1452-1477, March.
    2. Heungsun Hwang & Wayne Desarbo & Yoshio Takane, 2007. "Fuzzy Clusterwise Generalized Structured Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 181-198, June.
    3. Cristina Mollica & Luca Tardella, 2017. "Bayesian Plackett–Luce Mixture Models for Partially Ranked Data," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 442-458, June.
    4. 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.
    5. Biernacki, Christophe & Jacques, Julien, 2013. "A generative model for rank data based on insertion sort algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 162-176.
    6. John M. Mulvey & Harlan P. Crowder, 1979. "Cluster Analysis: An Application of Lagrangian Relaxation," Management Science, INFORMS, vol. 25(4), pages 329-340, April.
    7. Antonio D’Ambrosio & Sonia Amodio & Carmela Iorio & Giuseppe Pandolfo & Roberta Siciliano, 2021. "Adjusted Concordance Index: an Extensionl of the Adjusted Rand Index to Fuzzy Partitions," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 112-128, April.
    8. Lee, Paul H. & Yu, Philip L.H., 2012. "Mixtures of weighted distance-based models for ranking data with applications in political studies," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2486-2500.
    9. Eugenio Brentari & Livia Dancelli & Marica Manisera, 2016. "Clustering ranking data in market segmentation: a case study on the Italian McDonald's customers’ preferences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 1959-1976, August.
    10. Daniel Müllensiefen & Christian Hennig & Hedie Howells, 2018. "Using clustering of rankings to explain brand preferences with personality and socio-demographic variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(6), pages 1009-1029, April.
    11. Andrea Bonanomi & Marta Nai Ruscone & Silvia Angela Osmetti, 2017. "Defining subjects distance in hierarchical cluster analysis by copula approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 859-872, March.
    12. R. L. Plackett, 1975. "The Analysis of Permutations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(2), pages 193-202, June.
    13. Irurozki, Ekhine & Calvo, Borja & Lozano, Jose A., 2016. "PerMallows: An R Package for Mallows and Generalized Mallows Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i12).
    14. Murphy, Thomas Brendan & Martin, Donal, 2003. "Mixtures of distance-based models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 645-655, January.
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