Kernel-Based Nonlinear Subspace Method for Pattern Recognition.

A new pattern classification method called the Kernel-based Nonlinear Subspace (KNS) method is proposed. It implements a subspace method in a high-dimensional nonlinear space by a nonlinear transformation defined by kernel functions. The Support Vector Machine, a recent popular current research topic, is a nonlinear classification method employing kernel functions and has advanced classification performance. However, as the number of patterns and the number of classes increase, the problem faced is an explosive increase in the computational complexity needed for learning. Conventional subspace methods are effective classifiers of multiple classes and are fast classification techniques. But satisfactory classification performance is not achieved if the pattern distribution is nonlinear or if the dimensionality of the feature space is small compared to the number of classes. The proposed method combines the advantages of both techniques to compensate for each other's deficiencies to realize nonlinear classification of multiple classes with advanced classification performance and low computational complexity. In this paper, we demonstrate the ability to use nonlinear transforms defined by kernel functions to formulate the nonlinear subspace method, evaluate the proposed method from the perspectives of classification performance for nonlinear distributions and multiclass distributions, the stability of the classification performance with respect to parameter variations, and the computational costs needed for learning and classification, and verify the superiority of the proposed method over conventional methods. © 2001 Scripta Technica, Syst Comp Jpn, 33(1): 38–52, 2002 [ABSTRACT FROM AUTHOR]