Kernel Function Construction Based on Surface Reconstruction of Sample Similarity

In order to overcome the difficulties in constructing kernel function with data feature for current support vector machines(SVMs),this paper constructs three new kernel functions by reconstructing the similarity surface of data samples.It is proved that the first two are Mercer kernels,and the existence,stability and uniqueness of the three kernels are discussed.Kernel functions are in essence a tool to measure comparability,and there exists a mutually unnecessary and insufficient condition between kernel function,Mercer condition,positive definiteness and symmetry.Simulation shows that the presented kernel function can perfectly classify the learning samples,and its generalization ability is superior to the SVMs based on traditional kernel functions.