A kernelized discriminant analysis algorithm based on modified generalized singular value decomposition

The generalized singular value decomposition based linear discriminant analysis (LDA/GSVD) algorithm has been used to solve the singularity problem faced by the traditional LDA, but it is still computationally intensive in case of high dimensional patterns; and not applicable to the nonlinearly distributed patterns. In this paper, a new kernelized discriminant analysis algorithm based on a modified GSVD is proposed. In the proposed algorithm the original input space is implicitly mapped into a higher dimensional feature space from which features are extracted by using a modified GSVD which circumvents the calculation of the large-dimension singular vectors without losing the discriminative information. The proposed algorithm solves the nonlinear distribution problem and has the advantage of being computational efficient thanks to the new feature extraction method introduced in this paper. It is shown through extensive computer simulations on the typical pattern recognition benchmark databases that the proposed algorithm outperforms the existing linear algorithms and the kernelized ones.