Kernel generalized nonlinear discriminant analysis algorithm for pattern recognition

Linear discriminant analysis (LDA) is a very effective tool used for dimensionality reduction and feature extraction in pattern recognition. However, the LDA is inadequate to describe complex and nonlinear patterns. To solve this problem, kernel nonlinear discriminant analysis (K-NDA) has been proposed. Although successful in many cases, classic K-NDA also suffers from the small sample size problem (SSSP) and loses some significant discriminatory information as same as classic LDA. In this paper, a novel K-NDA, i.e., the kernel generalized nonlinear discriminant analysis (KG-NDA) algorithm is introduced to effectively overcome these problems and it also views the optimal discriminant vectors as a global transform in the feature space to some extent. It not only deals with the nonlinear problem, but also effectively solves the SSSP. The KG-NDA is applied to the experiments on face recognition and the results tested on two popular databases demonstrate that this method is very effective.