A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern classification: a unified view of statistical and neural approaches
Pattern classification: a unified view of statistical and neural approaches
Pattern Recognition Letters
Comparing partitions by means of fuzzy data mining tools
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
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Comparing partitions is an important issue in classification and clustering when comparing results from different methods, parameters, or initializations. A well-cestablished method for comparing partitions is the Rand index but this index is suitable for crisp partitions only. Recently, the Hüllermeier-Rifqi index was introduced which is a generalization of the Rand index to fuzzy partitions. In this paper we introduce a new approach to comparing partitions based on the similarities of their clusters in the sense of set similarity. All three indices, Rand, Hüllermeier-Rifqi, and subset similarity, are reflexive, invariant against row permutations, and invariant against additional empty subsets. The subset similarity index is not a generalization of the Rand index, but produces similar values. Subset similarity yields more intuitive similarities than Hüllermeier-Rifqi when comparing crisp and fuzzy partitions, and yields smoother nonlinear transitions. Finally, the subset similarity index has a lower computational complexity than the Hüllermeier-Rifqi index for large numbers of objects.