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Comparing High-Dimensional Partitions with the Co-clustering Adjusted Rand Index

Author

Listed:
  • Valerie Robert

    (Université Paris Saclay
    Université de la Réunion 2)

  • Yann Vasseur

    (Université Paris Saclay)

  • Vincent Brault

    (Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK)

Abstract

We consider the simultaneous clustering of rows and columns of a matrix and more particularly the ability to measure the agreement between two co-clustering partitions. The new criterion we developed is based on the Adjusted Rand Index and is called the Co-clustering Adjusted Rand Index named CARI. We also suggest new improvements to existing criteria such as the classification error which counts the proportion of misclassified cells and the Extended Normalized Mutual Information criterion which is a generalization of the criterion based on mutual information in the case of classic classifications. We study these criteria with regard to some desired properties deriving from the co-clustering context. Experiments on simulated and real observed data are proposed to compare the behavior of these criteria.

Suggested Citation

  • Valerie Robert & Yann Vasseur & Vincent Brault, 2021. "Comparing High-Dimensional Partitions with the Co-clustering Adjusted Rand Index," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 158-186, April.
    • Handle: RePEc:spr:jclass:v:38:y:2021:i:1:d:10.1007_s00357-020-09379-w
    DOI: 10.1007/s00357-020-09379-w
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    References listed on IDEAS

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    1. Wyse, Jason & Friel, Nial & Latouche, Pierre, 2017. "Inferring structure in bipartite networks using the latent blockmodel and exact ICL," Network Science, Cambridge University Press, vol. 5(1), pages 45-69, March.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. 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. C. Biernacki & J. Jacques & C. Keribin, 2023. "A Survey on Model-Based Co-Clustering: High Dimension and Estimation Challenges," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 332-381, July.
    2. Alessandro Casa & Charles Bouveyron & Elena Erosheva & Giovanna Menardi, 2021. "Co-clustering of Time-Dependent Data via the Shape Invariant Model," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 626-649, October.

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