Clustering Analysis of Multivariate Data: A Weighted Spatial Ranks-Based Approach

Determining the right number of clusters without any prior information about their numbers is a core problem in cluster analysis. In this paper, we propose a nonparametric clustering method based on different weighted spatial rank (WSR) functions. The main idea behind WSR is to define a dissimilarity measure locally based on a localized version of multivariate ranks. We consider a nonparametric Gaussian kernel weights function. We compare the performance of the method with other standard techniques and assess its misclassification rate. The method is completely data-driven, robust against distributional assumptions, and accurate for the purpose of intuitive visualization and can be used both to determine the number of clusters and assign each observation to its cluster.