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Fuzzy two-mode clustering: How to determine the optimal number of clusters?

Author

Listed:
  • Maria Brigida Ferraro

    (Sapienza University of Rome, Department of Statistical Sciences)

  • Paolo Giordani

    (Sapienza University of Rome, Department of Statistical Sciences)

  • Maurizio Vichi

    (Sapienza University of Rome, Department of Statistical Sciences)

Abstract

Two-mode clustering consists in simultaneously grouping rows and columns of an observed data matrix. In this context, an open problem is how to determine the optimal numbers of clusters of both partitions. The choice should consider the overall compactness and separation of the two-mode partition. In addition, if the fuzzy approach to clustering is adopted, the two membership degree matrices should assist in this task. For this reason, some cluster validity indices, taking into account the two objectives and the partitions’ fuzziness, are introduced and investigated. In particular, the well-known Partition Coefficient, Partition Entropy, Fuzzy Silhouette and Xie and Beni indices for standard (one-mode) fuzzy clustering and the here-proposed Fuzzy pseudo-F index are generalized to the fuzzy two-mode clustering framework. The adequacy of the proposed indices is checked by means of a simulation study and some applications.

Suggested Citation

  • Maria Brigida Ferraro & Paolo Giordani & Maurizio Vichi, 2026. "Fuzzy two-mode clustering: How to determine the optimal number of clusters?," Computational Statistics, Springer, vol. 41(2), pages 1-34, February.
    • Handle: RePEc:spr:compst:v:41:y:2026:i:2:d:10.1007_s00180-025-01691-6
    DOI: 10.1007/s00180-025-01691-6
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    References listed on IDEAS

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    1. Ferraro, Maria Brigida & Giordani, Paolo & Vichi, Maurizio, 2021. "A class of two-mode clustering algorithms in a fuzzy setting," Econometrics and Statistics, Elsevier, vol. 18(C), pages 63-78.
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