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One commonly used kernel in kernel-based support vector machine (SVM) approaches is radial basis function (RBF). This paper develops a weighted RBF (WRBF)-SVM by extending RBF kernels used by SVM to weighted RBF (WRBF) kernels by introducing a weighting matrix A into RBF kernels in which case there is no need of determining optimal values of parameters used in SVM, a long standing issue encountered in implementing SVM. A key to success in implementing WRBF kernels is to design different appropriate weighting matrices to implement WRBF kernels. Three weighting matrices are of particular interest, covariance matrix, correlation matrix and within-class scatter matrix. Experimental results demonstrate that WRBF kernels significantly improve over un-weighted RBF kernels in SVM-classification. Most importantly, WRBF-SVM offers a significant advantage over kernel-based SVM (KSVM) in that there is no need of determining optimal values of the parameters used by SVM.
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