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Minimum adjusted Rand index for two clusterings of a given size

Author

Listed:
  • José E. Chacón

    (Universidad de Extremadura)

  • Ana I. Rastrojo

    (Departamento de Matemáticas)

Abstract

The adjusted Rand index (ARI) is commonly used in cluster analysis to measure the degree of agreement between two data partitions. Since its introduction, exploring the situations of extreme agreement and disagreement under different circumstances has been a subject of interest, in order to achieve a better understanding of this index. Here, an explicit formula for the lowest possible value of the ARI for two clusterings of given sizes is shown, and moreover a specific pair of clusterings achieving such a bound is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:17:y:2023:i:1:d:10.1007_s11634-022-00491-w
    DOI: 10.1007/s11634-022-00491-w
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    References listed on IDEAS

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