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 $p$-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.

References in corpus (14)

• PCA consistency in high dimension, low sample size context
• Nonparametric multivariate rank tests and their unbiasedness
• Analysis of the duration--hardness ratio plane of gamma-ray bursts using skewed distributions
• Gaussian-mixture-model-based cluster analysis of gamma-ray bursts in the BATSE catalog
• Unsupervised classification of eclipsing binary light curves through k-medoids clustering
• A new measure for assessment of clustering based on kernel density estimation
• Distinction of groups of gamma-ray bursts in the BATSE catalog through fuzzy clustering
• Clustering of Gamma-Ray bursts through kernel principal component analysis
• Two phase formation of massive elliptical galaxies : study through cross-correlation including spatial effect
• A new nonparametric test for two sample multivariate location problem with application to astronomy
• Clustering of eclipsing binary light curves through functional principal component analysis
• A new nonparametric interpoint distance-based measure for assessment of clustering
• A new interpoint distance-based clustering algorithm using kernel density estimation
• Use of spatial cross correlation function to study formation mechanism of massive elliptical galaxies

Cited by in corpus (1)

• Confirmation of Binary Clustering in Gamma-Ray Bursts through an Integrated $p$-value from Multiple Nonparametric Tests of Hypotheses