An efficient Gaussian kernel optimization based on centered kernel polarization criterion

The success of kernel-based learning methods is heavily dependent on the choice of a kernel function and proper setting of its parameters. In this paper, we optimize the Gaussian kernel for binary-class problems by using centered kernel polarization criterion. This criterion is an extension of kernel polarization and a simplified style of centered kernel alignment. Compared with formulated kernel polarization criterion, the proposed criterion has a defined geometrical significance, and it can locate the global optimal point with less influence of threshold selection. Furthermore, the approximate criterion function can be proved to have a determined global minimum point by adopting the Euler-Maclaurin formula under weaker conditions. In addition, taking the preservation of within-class local structure into account, we present an evaluation criterion named local multiclass centered kernel polarization in multiclass classification scenario. Comparative experiments are conducted on some benchmark examples with three Gaussian kernel based learning methods and the results well demonstrate the effectiveness and efficiency of the proposed quality measures.