Development and evaluation of kernel-based clustering validity indices

In this paper, there are two objectives: on one hand, we extend four conventional validity indices, namely the DI, the II, the CH, and the GI, to four kernel-based validity indices, correspondingly, the kDI, the kII, the kCH and the kGI; on the other hand, we conduct a Monte-Carlo simulation to evaluate and compare these validity indices. The numerical results show that some kernel validity indices work significant better than conventional ones and some of the validity indices work poorly or do not work at all in our study.