Neighbor-rank densities for non-metric data

Abstract

In this work we propose rank densities, a novel density measure for non-metric data. Unlike typical measures employed in density clustering algorithms, rank densities are defined via ranks of patterns in k-nearest neighbor lists. Therefore they depend on the structure of the k-nearest neighbor graph, rather than exact values of the similarity measure. This property makes them robust to noise and easier to use with complicated similarity measures. We propose a simple iterative algorithm to estimate rank densities and demonstrate that it converges to a solution that does not depend on the initial configuration or the optimization step. Finally, we demonstrate an example application of rank densities to a real-world non-metric dataset.