Abstract
There have been various proposals on cluster validity functions but
they have not yet been compared using many numerical examples.
In this study we compare performances among different cluster validity functions.
That is, five measures of the sum of determinants and sum of traces of fuzzy covariances of clusters, Xie-Beni index, Davies-Bouldin index, and Fukuyama-Sugeno index as well as their kernelized versions are considered.
In particular, algorithms for calculating the kernelized measures are shown.
Effectiveness of these indices are compared using thousands of automatically generated clusters.
It will be shown that no single measure outperforms others,
and the sum of traces performs as good as that of determinants, contrary to the common understanding. Moreover, kernelized measures perform as well as non-kernelized ones.
