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arXiv · 2605.20806

Evaluation of the number of clusters in a data set using $p$-values from Multiple Tests of Hypotheses

Soumita Modak
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Abstract

This paper proposes a novel, nonparametric, interpoint distance-based measure to investigate whether there exist any groups in a set of given data, and if so then, how many groups are prevailing in total. It is a cluster accuracy index useful for arbitrary-dimensional data set, in association with any clustering algorithm having the number of groups specified as a priori. We perform univariate, nonparametric, multiple statistical tests of hypotheses, where as many dependent tests as the sample size are carried out using the interpoint distances. They possess $p$-values to be combined to reach a decision, which is taken in a step-wise process for a possible number of clusters. It reduces the unnecessary computations compared with the other accuracy measures from the literature. Data study establishes the proposed index's efficiency and superiority.

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Soumita Modak. 2026-05-20. Evaluation of the number of clusters in a data set using $p$-values from Multiple Tests of Hypotheses. https://doi.org/10.1080/03610926.2024.2309967

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