Evaluation of the number of clusters in a data set using $p$-values from Multiple Tests of Hypotheses
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 -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.
Keywords
Cite
@article{arxiv.2605.20806,
title = {Evaluation of the number of clusters in a data set using $p$-values from Multiple Tests of Hypotheses},
author = {Soumita Modak},
journal= {arXiv preprint arXiv:2605.20806},
year = {2026}
}