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A deflation-adjusted Bayesian information criterion for selecting the number of clusters in K-means clustering

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  • Ueki, Masao

Abstract

A deflation-adjusted Bayesian information criterion is proposed by introducing a closed-form adjustment to the variance estimate after K-means clustering. An expected lower bound of the deflation in the variance estimate after K-means clustering is derived and used as an adjustment factor for the variance estimates. The deflation-adjusted variance estimates are applied to the Bayesian information criterion under the Gaussian model for selecting the number of clusters. The closed-form expression makes the proposed deflation-adjusted Bayesian information criterion computationally efficient. Simulation studies show that the deflation-adjusted Bayesian information criterion performs better than other existing clustering methods in some situations, including K-means clustering with the number of clusters selected by standard Bayesian information criteria, the gap statistic, the average silhouette score, the prediction strength, and clustering using a Gaussian mixture model with the Bayesian information criterion. The proposed method is illustrated through a real data application for clustering human genomic data from the 1000 Genomes Project.

Suggested Citation

  • Ueki, Masao, 2025. "A deflation-adjusted Bayesian information criterion for selecting the number of clusters in K-means clustering," Computational Statistics & Data Analysis, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:csdana:v:209:y:2025:i:c:s0167947325000465
    DOI: 10.1016/j.csda.2025.108170
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    References listed on IDEAS

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    1. Hofmeyr, David P., 2020. "Degrees of freedom and model selection for k-means clustering," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    2. Batool, Fatima & Hennig, Christian, 2021. "Clustering with the Average Silhouette Width," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    3. Robert Thorndike, 1953. "Who belongs in the family?," Psychometrika, Springer;The Psychometric Society, vol. 18(4), pages 267-276, December.
    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. Sugar, Catherine A. & James, Gareth M., 2003. "Finding the Number of Clusters in a Dataset: An Information-Theoretic Approach," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 750-763, January.
    6. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
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