Systematic Analysis of Cluster Similarity Indices: Towards Bias-free Cluster Validation
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There are many cluster similarity indices used to evaluate clustering algorithms and choosing the best one for a particular task is usually an open problem. In this paper, we perform a thorough analysis of this problem: we develop a list of desirable properties (requirements) and theoretically verify which indices satisfy them. In particular, we investigate dozens of pair-counting indices and prove that none of them satisfies all the requirements. Based on our analysis, we propose using the arccosine of the correlation coefficient as a similarity measure and prove that it satisfies almost all requirements (except for one, which is still satisfied assymptotically). This new measure can be thought of as an angle between partitions.
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