A cluster validity measure with a hybrid parameter search method for the support vector clustering algorithm

This paper presents a cluster validity measure with a hybrid parameter search method for the support vector clustering (SVC) algorithm to identify an optimal cluster structure for a given data set. The cluster structure obtained by the SVC is controlled by two parameters: the parameter of kernel functions, denoted as q; and the soft-margin constant of Lagrangian functions, denoted as C. Large trial-and-error search efforts on these two parameters are necessary for reaching a satisfactory clustering result. From intensive observations of the behavior of the cluster splitting, we found that (1) the overall search range of q   is related to the densities of the clusters; (2) each cluster structure corresponds to an interval of q,q, and the size of each interval is different; and (3) identifying the optimal structure is equivalent to finding the largest interval among all intervals. We have based our findings on developing a validity measure with an ad hoc parameter search algorithm to enable the SVC algorithm to identify optimal cluster configurations with a minimal number of executions. Computer simulations have been conducted on benchmark data sets to demonstrate the effectiveness and robustness of our proposed approach.