Kernelized Xie-Beni index and its performance
Laizhao Hu · Kongzhi yu juece · 2007
With the help of the nonlinear mapping defined by kernel function implicitly, the noted Xie-Beni index for fuzzy c-means clustering is generalized into the kernel-defined Hilbert space. And the relation between the kernelized version of Xie-Beni and another index VLL is also investigated. Then, the performances and the dependencies of these two indices on Gauss kernel-width β and fuzzy exponent m are examined by some benchmark experiments, compared with two previously formulated indices, partition coefficient and partition entropy. The results show the superior performance and reliability of the kernelized Xie-Beni index in comparison to other indices, and it can take priority of being employed as the validity criterion for the kernel fuzzy clustering algorithm.