A Symmetric Purity Measure for Clustering Comparison

Abstract

Purity is frequently used to compare two clustering methods applied to a data set despite being an imbalanced measure that designates one clustering as correct. This paper introduces a new symmetric measure derived from Purity to evaluate clustering methods. Mathematical analysis demonstrates that this symmetric measure preserves properties similar to those of Purity. In addition, we conduct experiments to assess the robustness of various clustering algorithms to noise, including DBSCAN, HDBSCAN, K-means, K-medoids, Meanshift, deep clustering network, deep embedding for clustering and improved deep embedded clustering. Experimental results show that density-based clustering is not necessarily more robust to noise than other approaches for each possible case.