Pointwise norm-based clustering of data in arbitrary dimensional space

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.

KEYWORDS:

• Clustering algorithm
• pointwise norm
• arbitrary-dimensional data set
• nonparametric method
• bootstrapping
• high-dimensional applicability

Acknowledgments

The author would like to thank the Editor-in-Chief for encouraging the work and two anonymous reviewers for intriguing inquiries with valuable suggestions that helped the author to increase the quality of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.