IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v39y2022i2d10.1007_s00357-021-09407-3.html
   My bibliography  Save this article

On Assessments of Agreement Between Fuzzy Partitions

Author

Listed:
  • Jeffrey L. Andrews

    (University of British Columbia – Okanagan Campus)

  • Ryan Browne

    (University of Waterloo)

  • Chelsey D. Hvingelby

    (University of British Columbia – Okanagan Campus)

Abstract

We extend the literature regarding assessments of agreement between soft/fuzzy/probabilistic cluster allocations by providing closed-form approaches for two measures which behave as fuzzy generalizations of the popular adjusted Rand index (ARI): one novel and one previously requiring a Monte Carlo estimation process. Both of these measures retain the reflexive property of the ARI—an arguably essential property for the interpretability of a cluster agreement measure—and both are feasible in their closed-form for sample sizes ranging into five digits or more using standard consumer computers. We describe the approximate computational complexity in each case, and apply both measures in simulated and real data contexts.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jclass:v:39:y:2022:i:2:d:10.1007_s00357-021-09407-3
    DOI: 10.1007/s00357-021-09407-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00357-021-09407-3
    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/s00357-021-09407-3?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. Abby Flynt & Nema Dean & Rebecca Nugent, 2019. "sARI: a soft agreement measure for class partitions incorporating assignment probabilities," 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. 13(1), pages 303-323, March.
    2. Stephen Johnson, 1967. "Hierarchical clustering schemes," Psychometrika, Springer;The Psychometric Society, vol. 32(3), pages 241-254, September.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. 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)

    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. 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.
    2. 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.
    3. 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.
    4. 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".
    5. Martina Sundqvist & Julien Chiquet & Guillem Rigaill, 2023. "Adjusting the adjusted Rand Index," Computational Statistics, Springer, vol. 38(1), pages 327-347, March.
    6. Satoru Yokoyama & Atsuho Nakayama & Akinori Okada, 2009. "One-mode three-way overlapping cluster analysis," Computational Statistics, Springer, vol. 24(1), pages 165-179, February.
    7. Bocci, Laura & Vicari, Donatella & Vichi, Maurizio, 2006. "A mixture model for the classification of three-way proximity data," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1625-1654, April.
    8. 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.
    9. Weinand, J.M. & McKenna, R. & Fichtner, W., 2019. "Developing a municipality typology for modelling decentralised energy systems," Utilities Policy, Elsevier, vol. 57(C), pages 75-96.
    10. 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.
    11. Sun Jiehuan & Warren Joshua L. & Zhao Hongyu, 2017. "A Bayesian semiparametric factor analysis model for subtype identification," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(2), pages 145-158, April.
    12. 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.
    13. 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.
    14. Marco Berrettini & Giuliano Galimberti & Saverio Ranciati, 2023. "Semiparametric finite mixture of regression models with Bayesian P-splines," 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(3), pages 745-775, September.
    15. 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.
    16. Andrea Di Iura, 2022. "Comparison of empirical and shrinkage correlation algorithm for clustering methods in the futures market," SN Business & Economics, Springer, vol. 2(8), pages 1-17, August.
    17. Chia-Yi Chiu & Hans-Friedrich Köhn, 2016. "Consistency of Cluster Analysis for Cognitive Diagnosis: The Reduced Reparameterized Unified Model and the General Diagnostic Model," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 585-610, September.
    18. İsmail Güzel & Atabey Kaygun, 2022. "A new non-archimedean metric on persistent homology," Computational Statistics, Springer, vol. 37(4), pages 1963-1983, September.
    19. 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.
    20. José E. Chacón & Ana I. Rastrojo, 2023. "Minimum adjusted Rand index for two clusterings of a given size," 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 125-133, 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:39:y:2022:i:2:d:10.1007_s00357-021-09407-3. 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.