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Many different measures proposed for cluster validity remain to be compared using sufficient numbers of numerical examples. We compare the performance of five measures of the sum of determinants and the sum of traces of fuzzy covariances of clusters, the Xie-Beni index, the Davies-Bouldin index, and the Fukuyama-Sugeno index together with their kernelized versions, focusing on algorithms for calculating kernelized measures. We compared the effectiveness of these indices using thousands of automatically generated clusters. We found that no single measure outperforms the others, and that, contrary to the common understanding that determinants are better than traces, the sum of traces performs as well as the sum of determinants and, kernelized measures perform as well as nonkernelized ones.

Comparison and Evaluation of Different Cluster Validity Measures Including Their Kernelization