Despite the excellent applicability of kernel methods, there seems to be no systematic way of choosing appropriate kernel functions or the optimum parameters. Therefore, the performance of support vector machines (SVMs) cannot be easily optimized. To address this problem, a general procedure is suggested to produce nonparametric and efficient kernels. This is achieved by finding an empirical and theoretical connection between positive semidefinite matrices and certain metric space properties. The Gaussian kernel turns out to be a special case of the new framework. Comprehensive experiments on eleven realworld datasets and seven synthetic datasets demonstrate a clear advantage in favor of the proposed kernels. However, several important problems remain unresolved.