A new Mallows distance based metric for comparing clusterings

Authors:
Ding Zhou;Jia Li;Hongyuan Zha
Affiliations:
The Pennsylvania State University, University Park, PA;The Pennsylvania State University, University Park, PA;The Pennsylvania State University, University Park, PA
Venue:
ICML '05 Proceedings of the 22nd international conference on Machine learning
Year:
2005

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Abstract

Despite of the large number of algorithms developed for clustering, the study on comparing clustering results is limited. In this paper, we propose a measure for comparing clustering results to tackle two issues insufficiently addressed or even overlooked by existing methods: (a) taking into account the distance between cluster representatives when assessing the similarity of clustering results; (b) constructing a unified framework for defining a distance based on either hard or soft clustering and ensuring the triangle inequality under the definition. Our measure is derived from a complete and globally optimal matching between clusters in two clustering results. It is shown that the distance is an instance of the Mallows distance---a metric between probability distributions in statistics. As a result, the defined distance inherits desirable properties from the Mallows distance. Experiments show that our clustering distance measure successfully handles cases difficult for other measures.