A new interpoint distance-based clustering algorithm using kernel density estimation

Abstract

A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric univariate kernel density estimation method to the interpoint distances to estimate the density around a data member. Our clustering algorithm is simple in its formation and easy to apply resulting in well-defined clusters. The algorithm starts with objective selection of the initial cluster representative and always converges independently of this choice. The method finds the number of clusters itself and can be used irrespective of the nature of underlying data by using an appropriate interpoint distance measure. The cluster analysis can be carried out in any dimensional space with viability to high-dimensional use. The distributions of the data or their interpoint distances are not required to be known due to the design of our procedure, except the assumption that the interpoint distances possess a density function. Data study shows its effectiveness and superiority over the widely used clustering algorithms.

Keywords:

• Clustering algorithm
• Interpoint distance
• Nonparametric method
• Kernel density estimator
• High-dimensional applicability

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62H30

Acknowledgments

The author would like to express her sincere gratitude to the Editor-in-chief to encourage the work. Author greatly acknowledges an anonymous associate editor for meticulous judgment, proficient advice, considerate appreciation of the significance regarding the present work and for giving the opportunity for its revision. The author feels short of words to thank enough the three esteemed (anonymous) reviewers to read the manuscript to its intrinsic details and kindly provide their expert feedback that helped to draw the author’s attention to the potential improvements and to revise the manuscript to a substantial degree which increased its exposition.

Disclosure statement

No potential conflict of interest was reported by the author.