Weighted Gaussian Kernel With Multiple Widths And Its Support Vector Classification And Network Kernel Pattern

Pattern Analysis, as one of the most important branch of Artificial Intelligence and Machine Learning, is widely used in Industrial Expert System, Biological Genetic Information Science, Cosmology, Astronomy and Robot Technology. Especially when computing speed is not the main bottle neck of Von·Neumann architected computers, ability of self learning by machines is the focus by now. People have been trying to find solutions back into Artificial Intelligence and Machine Learning. Pattern Analysis, as the most basic ability should be addressed by all Artificial Intelligence and Machine Learning related machines firstly. One of the most widely used algorithms of Pattern Analysis is Support Vector Machines, which has been proved with better effect than traditional algorithms, as well as stronger statistical theories support. Kernel Function, as one of the most important ways of non-linear mapping, is the essence of Support Vector Machines with such wide application. An independent discipline called Kernel Methods has been formed especially for kernel functions. The purpose of this thesis is to research the properties and construction of kernel functions. Research of kernel functions does not only improve the usage of Support Vector Machines, but also gives support to Artificial Intelligence and Machine Learning themselves.The relationship between Support Vector Machines and Kernel Methods has been displayed in this thesis. According to the defect of Gaussian kernel, that is unable to distinguish the different importance of features, a new kernel function called Weighted Gaussian Kernel with Multiple Widths (WGKMW) has been proposed and proved to be a legal kernel function in Kernel Methods. Referring to Radius Margin Error Bound and Quasi-Newton Gradient Descent model, a new algorithm has been proposed to determine the parameters of WGKMW. Based on the Radius Basis Function Network (RBFN) architecture of WGKMW, a new framework called Network Kernel Pattern (NKP) has been proposed to construct a new class of kernel functions. The essence of NKP is a RBFN with fixed relative weights. Via precise comparison from Support Vector Classification experiments between WGKMW and Gaussian Kernel, WGKMW showed better effects than Gaussian Kernel. Through classification hyper plane comparison from Support Vector Classification experiments between applying NKP on Polynomial Kernel and Gaussian Kernel and original ones, the advantages of multiple parameters of NKP have been revealed.