Pointwise norm-based clustering of data in arbitrary dimensional space

Abstract

ABSTRACT In this paper, a novel nonparametric norm-based clustering algorithm is proposed to classify real-valued continuous data sets given in arbitrary dimensional space. For data univariate, multivariate or high-dimensional, with the number of study variables close to or larger than the data size, our straightforward algorithm is implemented throughout under an univariate set-up, where we make use of the observation-wise (or pointwise) norms which quantify the distances of the observations from the origin zero or the null vector. The method begins with determination of the sample quantile using nonparamteric bootstrapping on the computed norms and always converges independently. By its design, the suggested algorithm is fast enough to detect the number of existing clusters itself and to form well-defined groups. Data study demonstrates its competitiveness in comparison to 2 popular clustering algorithms K-means and K-medoids.