Nonparametric Nearest Neighbor Descent Clustering based on Delaunay Triangulation

Abstract: In our physically inspired in-tree (IT) based clustering algorithm and the series after it, there is only one free parameter involved in computing the potential value of each point. In this work, based on the Delaunay Triangulation or its dual Voronoi tessellation, we propose a nonparametric process to compute potential values by the local information. This computation, though nonparametric, is relatively very rough, and consequently, many local extreme points will be generated. However, unlike those gradient-based methods, our ITbased methods are generally insensitive to those local extremes. This positively demonstrates the superiority of these parametric (previous) and nonparametric (in this work) ITbased methods. 1 Introduction In (1), we proposed a physically inspired clustering algorithm, in which an in-tree (IT) structure was first constructed. This IT structure organizes the data points into the clusters with several undesired connections (edges) between them requiring to be removed.