A Density-Penalized Distance Measure for Clustering

Abstract

Measure of similarity between objects plays an important role in clustering. Most of the clustering methods use Euclidean metric as a measure of distance. However, due to the limitations of the partitioning clustering methods, another family of clustering algorithms called density-based methods has been developed. This paper introduces a new distance measure that equips the distance function with a density-aware component. This distance measure, called Density-Penalized Distance (DPD), is a regularized Euclidean distance that adds a penalty term to Euclidean distance based on the difference between the densities around the two points. The intuition behind the idea is that if the densities around two points differ from each other, they are less likely to belong to same cluster. A new point density estimation method, an analysis on the computational complexity of the algorithm in addition to theoretical analysis of the distance function properties are also provided in this work. Experiments were conducted in five different clustering algorithms and the results of DPD are compared with that obtained by using three other standard distance measures. Nine different UCI datasets were used for evaluation. The results show that the performance of DPD is significantly better or at least comparable to the classical distance measures.