IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v38y2021i1d10.1007_s00357-020-09367-0.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00357-020-09367-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00357-020-09367-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. J. Gower & P. Legendre, 1986. "Metric and Euclidean properties of dissimilarity coefficients," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 5-48, March.
    3. Fortunato Pesarin & Luigi Salmaso, 2010. "The permutation testing approach: a review," Statistica, Department of Statistics, University of Bologna, vol. 70(4), pages 481-509.
    4. Matthijs Warrens, 2008. "On Association Coefficients for 2×2 Tables and Properties That Do Not Depend on the Marginal Distributions," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 777-789, December.
    5. Adi Ben-Israel & Cem Iyigun, 2008. "Probabilistic D-Clustering," Journal of Classification, Springer;The Classification Society, vol. 25(1), pages 5-26, June.
    6. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Giuseppe Pandolfo & Antonio D’ambrosio, 2023. "Clustering directional data through depth functions," Computational Statistics, Springer, vol. 38(3), pages 1487-1506, September.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Isabella Morlini & Sergio Zani, 2012. "Dissimilarity and similarity measures for comparing dendrograms and their applications," 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. 6(2), pages 85-105, July.
    2. Jonathon J. O’Brien & Michael T. Lawson & Devin K. Schweppe & Bahjat F. Qaqish, 2020. "Suboptimal Comparison of Partitions," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 435-461, July.
    3. Andrzej Młodak, 2021. "k-Means, Ward and Probabilistic Distance-Based Clustering Methods with Contiguity Constraint," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 313-352, July.
    4. Matthijs J. Warrens & Alexandra de Raadt, 2015. "Ordering Properties of the First Eigenvector of Certain Similarity Matrices," Journal of Mathematics, Hindawi, vol. 2015, pages 1-5, November.
    5. 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.
    6. Isabella Morlini & Sergio Zani, 2012. "A New Class of Weighted Similarity Indices Using Polytomous Variables," Journal of Classification, Springer;The Classification Society, vol. 29(2), pages 199-226, July.
    7. José E. Chacón, 2021. "Explicit Agreement Extremes for a 2 × 2 Table with Given Marginals," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 257-263, July.
    8. Stefano Tonellato & Andrea Pastore, 2013. "On the comparison of model-based clustering solutions," Working Papers 2013:05, Department of Economics, University of Venice "Ca' Foscari".
    9. Douglas L. Steinley & M. J. Brusco, 2019. "Using an Iterative Reallocation Partitioning Algorithm to Verify Test Multidimensionality," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 397-413, October.
    10. Martina Sundqvist & Julien Chiquet & Guillem Rigaill, 2023. "Adjusting the adjusted Rand Index," Computational Statistics, Springer, vol. 38(1), pages 327-347, March.
    11. Florian Schreiber, 2017. "Identification of customer groups in the German term life market: a benefit segmentation," Annals of Operations Research, Springer, vol. 254(1), pages 365-399, July.
    12. Matthijs J. Warrens, 2014. "New Interpretations of Cohen’s Kappa," Journal of Mathematics, Hindawi, vol. 2014, pages 1-9, September.
    13. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    14. Matthijs Warrens, 2008. "On Association Coefficients for 2×2 Tables and Properties That Do Not Depend on the Marginal Distributions," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 777-789, December.
    15. Daniel Baier & Ines Daniel & Sarah Frost & Robert Naundorf, 2012. "Image data analysis and classification in marketing," 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. 6(4), pages 253-276, December.
    16. Matthijs J. Warrens & Hanneke Hoef, 2022. "Understanding the Adjusted Rand Index and Other Partition Comparison Indices Based on Counting Object Pairs," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 487-509, November.
    17. Jeffrey L. Andrews & Ryan Browne & Chelsey D. Hvingelby, 2022. "On Assessments of Agreement Between Fuzzy Partitions," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 326-342, July.
    18. Ekaterina Kovaleva & Boris Mirkin, 2015. "Bisecting K-Means and 1D Projection Divisive Clustering: A Unified Framework and Experimental Comparison," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 414-442, October.
    19. Matthijs J. Warrens, 2016. "Inequalities Between Similarities for Numerical Data," Journal of Classification, Springer;The Classification Society, vol. 33(1), pages 141-148, April.
    20. Theresa Ullmann & Anna Beer & Maximilian Hünemörder & Thomas Seidl & Anne-Laure Boulesteix, 2023. "Over-optimistic evaluation and reporting of novel cluster algorithms: an illustrative study," 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. 17(1), pages 211-238, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jclass:v:38:y:2021:i:1:d:10.1007_s00357-020-09367-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.