Weighted Gaussian Kernel with Multiple Widths and Support Vector Classifications

As an important kernel function in support vector machines (SVM), Gaussian kernel (GK) is widely used in pattern recognition and artificial intelligence. However, the fact that Gaussian kernel could not distinguish the importance of data features is not conforming to the practical situation. According to the deficiency of Gaussian kernel, weighted Gaussian kernel with multiple widths (WGKMW) is proposed and proven to be a legal kernel in kernel methods. Results of experiments for support vector classifications with WGKMW are revealed better performances comparing with GK. According to the error bound and Newton gradient descent methods, simple error bound with model selection method (SEBWMS) is proposed to determine the multiple parameters of WGKMW at the end of the passage.