Design Of Adaptive Kernels For Support Vector Machine

Support vector machine is a good learning machine based on the statistical learning theory. In linear classification, it find the super hyperplane between with two-class samples in the input space. In nonlinear classification, it map the input data into a high-dimensional feature space ,and then find the super hyperplane in feature space. A good property of SVM is that we need not compute the mapped patterns explicitly, and instead we only need the dot products between mapped patters, which are directly available from the kernel function. It combine hyperplane of maximizing margin, Mercer kernel with flabby variable and the sparse solution, so have good performance in many defiant problem about machine learning .In order to gain the best generalization ability ,SVM find the best compromise between with complexity of model and learning ability by using the information of finite samples.A remaining problem is that the performance of support vector machine(SVM) largely depends on the kernel, but there have been no theories concerning how to choose a good kernel in a data-dependent way. in order to gain a better intuitive understanding of how one's data is being mapped, we exploring the geometry of support vector methods by using geometry analysis of Riemanninan ,and then we get the method for adaptive kernel by modify the Riemanninan metric .In this paper , The adaptive kernel function is conformally transformaled in a data-dependent way by using the information of support vectors in primary training.Base on the front we gain the adaptive kernel by using the points of error classified and the support vectors that not on the standard plan, and then we get the kernel which base on the density around the support vectors. At last we compare the kernels by using simulation results for both artificial and real data .