A Dynamic Weighted Sum Validity Function for Fuzzy Clustering with an Adaptive Differential Evolution Algorithm

Clustering is a difficult problem, both with respect to the construction of adequate objective functions as well as to the optimization of the objective functions. In this article, the weighted sum validity function (WSVF) is improved as a dynamic weighted sum validity function(DWSVF) to evaluate fuzzy partitioning. Moreover, we proposed an adaptive differential evolution algorithm, which can be used for the optimization of the DWSVF in fuzzy partitioning. Finally, several artificial data sets are used to test the performance of the proposed index (DWSVF) and the performance of the adaptive differential evolution algorithm. The experimental results show that DWSVF is effective. Compared with three fuzzy cluster validity functions, DWSVF achieves more accurate and robust results.