Weighted Gaussian Kernel with Multiple Widths and Network Kernel Pattern

Abstract

Traditional Gaussian Kernel is the most widely used in Kernel Machines, such as Support Vector Machines and has been extensively studied in the field of Neural Networks, such as Radial Basis Function Network. However, because of the same weight and data distribution defined in traditional Gaussian Kernel, the weights of Neural Network based on such kernels are controlled mostly by the input data. There is no difference between the Activation Function(that is, Neuron or Neurode). We propose a new kernel called Weighted Gaussian Kernel with Multiple Widths to have more parameters to control the data. Using the new kernel in Neural Networks, we propose a new conception call Network Kernel Pattern to improve the traditional structure of Radial Basis Function Network with some new definitions.