Multi-category classification by kernel based nonlinear subspace method

The Kernel based Nonlinear Subspace (KNS) method is proposed for multi-class pattern classi cation. This method consists of the nonlinear transformation of feature spaces de ned by kernel functions and subspace method in transformed high-dimensional spaces. The Support Vector Machine, a nonlinear classi er based on a kernel function technique, shows excellent classi cation performance, however, its computational cost increases exponentially with the number of patterns and classes. The linear subspace method is a technique for multi-category classi cation, but it fails when the pattern distribution has nonlinear characteristics or the feature space dimension is low compared to the number of classes. The proposed method combines the advantages of both techniques and realizes multi-class nonlinear classi ers with better performance in less computational time. In this paper, we show that a nonlinear subspace method can be formulated by nonlinear transformations de ned through kernel functions and that its performance is better than that obtained by conventional methods.