IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v37y2020i2d10.1007_s00357-019-09329-1.html
   My bibliography  Save this article

Suboptimal Comparison of Partitions

Author

Listed:
  • Jonathon J. O’Brien

    (Harvard Medical School)

  • Michael T. Lawson

    (University of North Carolina at Chapel Hill)

  • Devin K. Schweppe

    (Harvard Medical School)

  • Bahjat F. Qaqish

    (University of North Carolina at Chapel Hill)

Abstract

The distinction between classification and clustering is often based on a priori knowledge of classification labels. However, in the purely theoretical situation where a data-generating model is known, the optimal solutions for clustering do not necessarily correspond to optimal solutions for classification. Exploring this divergence leads us to conclude that no standard measures of either internal or external validation can guarantee a correspondence with optimal clustering performance. We provide recommendations for the suboptimal evaluation of clustering performance. Such suboptimal approaches can provide valuable insight to researchers hoping to add a post hoc interpretation to their clusters. Indices based on pairwise linkage provide the clearest probabilistic interpretation, while a triplet-based index yields information on higher level structures in the data. Finally, a graphical examination of receiver operating characteristics generated from hierarchical clustering dendrograms can convey information that would be lost in any one number summary.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:2:d:10.1007_s00357-019-09329-1
    DOI: 10.1007/s00357-019-09329-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00357-019-09329-1
    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/s00357-019-09329-1?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. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    2. F. Baulieu, 1989. "A classification of presence/absence based dissimilarity coefficients," Journal of Classification, Springer;The Classification Society, vol. 6(1), pages 233-246, December.
    3. Yujin Hoshida & Jean-Philippe Brunet & Pablo Tamayo & Todd R Golub & Jill P Mesirov, 2007. "Subclass Mapping: Identifying Common Subtypes in Independent Disease Data Sets," PLOS ONE, Public Library of Science, vol. 2(11), pages 1-8, November.
    4. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    5. Christian Hennig & Tim F. Liao, 2013. "How to find an appropriate clustering for mixed-type variables with application to socio-economic stratification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(3), pages 309-369, May.
    6. John Daws, 1996. "The analysis of free-sorting data: Beyond pairwise cooccurrences," Journal of Classification, Springer;The Classification Society, vol. 13(1), pages 57-80, March.
    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.
    8. 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.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Batool, Fatima & Hennig, Christian, 2021. "Clustering with the Average Silhouette Width," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    8. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    9. Yaeji Lim & Hee-Seok Oh & Ying Kuen Cheung, 2019. "Multiscale Clustering for Functional Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 368-391, July.
    10. 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".
    11. Elvira Pelle & Roberta Pappadà, 2021. "A clustering procedure for mixed-type data to explore ego network typologies: an application to elderly people living alone in Italy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1507-1533, December.
    12. Roberto Mari & Roberto Rocci & Stefano Antonio Gattone, 2020. "Scale-constrained approaches for maximum likelihood estimation and model selection of clusterwise linear regression models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 49-78, March.
    13. 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.
    14. 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.
    15. Martina Sundqvist & Julien Chiquet & Guillem Rigaill, 2023. "Adjusting the adjusted Rand Index," Computational Statistics, Springer, vol. 38(1), pages 327-347, March.
    16. 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.
    17. Hennig, Christian, 2008. "Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1154-1176, July.
    18. J. Fernando Vera & Rodrigo Macías, 2021. "On the Behaviour of K-Means Clustering of a Dissimilarity Matrix by Means of Full Multidimensional Scaling," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 489-513, June.
    19. Douglas Steinley & Michael Brusco, 2008. "Selection of Variables in Cluster Analysis: An Empirical Comparison of Eight Procedures," Psychometrika, Springer;The Psychometric Society, vol. 73(1), pages 125-144, March.
    20. Andrea Cerasa, 2016. "Combining homogeneous groups of preclassified observations with application to international trade," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(3), pages 229-259, August.

    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:37:y:2020:i:2:d:10.1007_s00357-019-09329-1. 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.