New empirical nonparametric kernels for support vector machine classification

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 real-world datasets and seven synthetic datasets demonstrate a clear advantage in favor of the proposed kernels. However, several important problems remain unresolved.

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► A potential disadvantage of using the SVM is that there is no an efficient way to find a perfect kernel and its parameters for a given application.
► To overcome this restriction, a new framework for designing efficient kernels is introduced.
► By using the new procedure, unlimited number of practical kernels can be generated.
► The suggested kernels can be applied without parameters.