Research On Basic Methods Of Construction Of Feature Space Related To Indefinite Kernels

The indefinite kernels used in Support vector machine(SVM) are being concerned seriously.However,they are barely to be explained for missing theoretical foundations and geometrical understanding.In order that interpret why indefinite kernels are useful in the classification problem.In this paper,we generalize the Mercer theorem,which the eigenvalues can be negative,and the proof of the theorem is given.We discuss the construction of feature space related to indefinite kernels by two methods,such as,the way of generalization about the Mercer theorem,the method of power series expression.At the same time,we develop the Pseudo-Euclidean space to Krein space,which dimensions is infinite. State the support vector machine in feature space related to indefinite kernel.