Fully Data-Driven Optimization of Gaussian Parameters for Kernel Classifier

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This paper establishes a fully data-driven online estimation method of Gaussian kernel parameters for a kernel logistic regression. The kernel logistic regression is a nonlinear classification model that effectively uses kernel methods, which are one of the techniques to construct effective nonlinear systems with a reproducing kernel Hilbert space (RKHS) induced from a positive semi-definite kernel. Since a performance of the kernel logistic regression with RKHS depends on the kernels to build the model, it is important to select appropriate kernel parameters. In this paper, we propose a method to optimize the precisions (the preciprocal of the variance) at learning for the kernel logistic regression using Gaussian kernels. In addition, the kernel means are also updated to increase the generalization ability. For up to date method of kernel coefficients, we introduce $\ell_{1}$ -regularization to supress the number of support vectors. A numerical experiment supports the validity of the proposed method.

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