Kernel Discriminant Analysis based on Generalized Singular Value Decomposition

Abstract

In Linear Discriminant Analysis (LDA), a dimension reducing linear transformation is found in order to better distinguish clusters from each other in the reduced dimensional space. However, LDA has a limitation that one of the scatter matrices is required to be nonsingular and the nonlinearly clustered structure is not easily captured. We propose a nonlinear discriminant analysis based on kernel functions and the generalized singular value decomposition called KDA/GSVD, which is a nonlinear extension of LDA and works regardless of the nonsingularityof the scatter matrices in either the input space or feature space. Our experimental results show that our method is a very effective nonlinear dimension reduction method.