Multi-category classification by kernel based nonlinear subspace method

The kernel based nonlinear subspace (KNS) method is proposed for multi-class pattern classification. This method consists of the nonlinear transformation of feature spaces defined by kernel functions and subspace method in transformed high-dimensional spaces. The support vector machine, a nonlinear classifier based on a kernel function technique, shows excellent classification performance, however, its computational cost increases exponentially with the number of patterns and classes. The linear subspace method is a technique for multi-category classification, 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 classifiers with better performance in less computational time. We show that a nonlinear subspace method can be formulated by nonlinear transformations defined through kernel functions and that its performance is better than that obtained by conventional methods