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Adjusted Concordance Index: an Extensionl of the Adjusted Rand Index to Fuzzy Partitions

Author

Listed:
  • Antonio D’Ambrosio

    (University of Naples Federico II)

  • Sonia Amodio

    (Leiden University Medical Center)

  • Carmela Iorio

    (University of Naples Federico II)

  • Giuseppe Pandolfo

    (University of Naples Federico II)

  • Roberta Siciliano

    (University of Naples Federico II)

Abstract

In comparing clustering partitions, the Rand index (RI) and the adjusted Rand index (ARI) are commonly used for measuring the agreement between partitions. Such external validation indexes can be used to quantify how close the clusters are to a reference partition (or to prior knowledge about the data) by counting classified pairs of elements. To evaluate the solution of a fuzzy clustering algorithm, several extensions of the Rand index and other similarity measures to fuzzy partitions have been proposed. An extension of the ARI for fuzzy partitions based on the normalized degree of concordance is proposed. The performance of the proposed index is evaluated through Monte Carlo simulation studies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jclass:v:38:y:2021:i:1:d:10.1007_s00357-020-09367-0
    DOI: 10.1007/s00357-020-09367-0
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    References listed on IDEAS

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    1. Ahmed Albatineh & Magdalena Niewiadomska-Bugaj, 2011. "Correcting Jaccard and other similarity indices for chance agreement in cluster analysis," 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(3), pages 179-200, October.
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    5. Ahmed N. Albatineh & Magdalena Niewiadomska-Bugaj & Daniel Mihalko, 2006. "On Similarity Indices and Correction for Chance Agreement," Journal of Classification, Springer;The Classification Society, vol. 23(2), pages 301-313, September.
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    Cited by:

    1. Giuseppe Pandolfo & Antonio D’ambrosio, 2023. "Clustering directional data through depth functions," Computational Statistics, Springer, vol. 38(3), pages 1487-1506, September.
    2. 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.
    3. Carmela Iorio & Gianluca Frasso & Antonio D’Ambrosio & Roberta Siciliano, 2023. "Boosted-oriented probabilistic smoothing-spline clustering of series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1123-1140, October.

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