Properties and Construction Methods of Kernel in Support Vector Machine
核函数的性质及其构造方法

Support vector machine, which has been successfully applied to pattern recognition, regression estimation, cluster and so on, is a typical instance of kernel method. It is completely characterized by kernel function and training set. The key to enhance performance of support vector machine is to choose an appropriate kernel function for the given problem; therefore deep understanding to kernel itself is needed. Firstly, this paper analyzes some important properties of kernel, and then proposes criterions for judgment of three classes of kernel function, i.e. translation invariant, rotation invariant and convolution kernels. By them, a lot of important kernel functions are constructed some of which are commonly employed in practice.