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A Note on Maximizing the Agreement Between Partitions: A Stepwise Optimal Algorithm and Some Properties

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  • Douglas Steinley
  • Gretchen Hendrickson
  • Michael Brusco

Abstract

Building on Brusco and Steinley (2008), a computationally efficient stepwise optimal heuristic is provided for maximizing the adjusted Rand index (Hubert and Arabie 1985). The proposed algorithm is different than other methods for estimating the maximum value for the adjusted Rand index (e.g., Messatfa 1992) in that it does not rely on mathematical programming; consequently, problems of much larger size can be handled. Using the proposed method, various characteristics of the adjusted Rand index are explored and presented. Copyright Classification Society of North America 2015

Suggested Citation

  • Douglas Steinley & Gretchen Hendrickson & Michael Brusco, 2015. "A Note on Maximizing the Agreement Between Partitions: A Stepwise Optimal Algorithm and Some Properties," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 114-126, April.
    • Handle: RePEc:spr:jclass:v:32:y:2015:i:1:p:114-126
    DOI: 10.1007/s00357-015-9169-z
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    References listed on IDEAS

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    1. Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 159-179, June.
    2. H. Messatfa, 1992. "An algorithm to maximize the agreement between partitions," Journal of Classification, Springer;The Classification Society, vol. 9(1), pages 5-15, January.
    3. Glenn Milligan & Richard Cheng, 1996. "Measuring the influence of individual data points in a cluster analysis," Journal of Classification, Springer;The Classification Society, vol. 13(2), pages 315-335, September.
    4. Michael Brusco & Douglas Steinley, 2008. "A Binary Integer Program to Maximize the Agreement Between Partitions," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 185-193, November.
    5. Douglas Steinley & Michael J. Brusco, 2007. "Initializing K-means Batch Clustering: A Critical Evaluation of Several Techniques," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 99-121, June.
    6. Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 249-270, June.
    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.
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    Cited by:

    1. 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.
    2. Santi, Éverton & Aloise, Daniel & Blanchard, Simon J., 2016. "A model for clustering data from heterogeneous dissimilarities," European Journal of Operational Research, Elsevier, vol. 253(3), pages 659-672.
    3. 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.
    4. Salvatore Ingrassia & Antonio Punzo, 2020. "Cluster Validation for Mixtures of Regressions via the Total Sum of Squares Decomposition," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 526-547, July.
    5. 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.

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