Graph Sensitive Indices for Comparing Clusterings

TL;DR

This paper introduces two novel clustering comparison indices, RWI and VIN, which incorporate data point positions and are inspired by the Variation of Information metric, offering potentially more meaningful clustering evaluations.

Contribution

The paper proposes two new indices, RWI and VIN, that consider data point positions for comparing clusterings, extending existing set-based methods.

Findings

RWI and VIN provide alternative perspectives on clustering similarity.

Both indices show promising properties in theoretical analysis.

Experimental results demonstrate their applicability on example datasets.

Abstract

This report discusses two new indices for comparing clusterings of a set of points. The motivation for looking at new ways for comparing clusterings stems from the fact that the existing clustering indices are based on set cardinality alone and do not consider the positions of data points. The new indices, namely, the Random Walk index (RWI) and Variation of Information with Neighbors (VIN), are both inspired by the clustering metric Variation of Information (VI). VI possesses some interesting theoretical properties which are also desirable in a metric for comparing clusterings. We define our indices and discuss some of their explored properties which appear relevant for a clustering index. We also include the results of these indices on clusterings of some example data sets.