Classical Self-Organizing Maps presented by T.Kohonen is performed in the input sample space based on the Euclidean norm.It fails as the distrubution of input patterns becomes highly nonlinear.Kernel means

performing a nonlinear data transformation into some high dimensional feature space

increases the probability of the linear separability of the patterns within the feature space.Donald and others map the data in input space into a high-dimension feature space

where SOM algorithm are performed.However

its disadvantage lies in lack of direct descriptions about the clustering's center and result.In this paper

a novel kernel-based SOM algorithm is proposed.we replace the Euclidean norm in the SOM training procedure with kernels

which is equivalent to change the metric of distance in input space.Multiformity of kernels leads to different metrics of distance in input space

and correspondingly results in SOM classifications.Finally we discuss the robustness and reliablity of KSOM by experimenting on Benchmark based on several classical kernel functions.