Optimizing Kernel-Based Nonlinear Subspace Methods Using Prototype Reduction Schemes

Abstract

The subspace method of pattern recognition is a classification technique in which pattern classes are specified in terms of linear subspaces spanned by their respective class-based basis vectors. To overcome the limitations of the linear methods, Kernel based Nonlinear Subspace (KNS) methods have been recently proposed in the literature. In KNS, the kernel Principal Component Analysis (kPCA) has been employed to get principal components, not in an input space, but in a highdimensional space, where the components of the space are non-linearly related to the input variables.In this paper, we suggest a computationally superior mechanism to solve the problem. Rather than define the matrix K with the whole data set and compute the principal components, we propose that the data be reduced into a smaller representative subset using a Prototype Reduction Scheme (PRS). Our experimental results demonstrate that the proposed mechanism dramatically reduces the computation time without sacrificing the classification accuracy for samples involving real-life data sets as well as artificial data sets. The results especially demonstrate the computational advantage for large data sets, such as those involved in data mining and text categorization applications.KeywordsKernel Principal Component Analysis (kPCA)Kernelbased Nonlinear Subspace (KNS) MethodPrototype Reduction Schemes(PRS).