Local linear discriminant analysis with composite kernel for face recognition

This paper presents a method for nonlinear discriminant analysis utilizing a composite kernel which is derived from a combination of local linear models with interpolation. The underlying idea is to decompose a complex nonlinear problem into a set of simpler local linear problems. Combining with the theory of nonlinear classification based on kernels, the local linear models with interpolation can be formulated as a composite kernel based discriminant analysis form. In face recognition, linear discriminant analysis (LDA) has been widely adopted owing to its efficiency, but it fails to solve nonlinear problems. Conventional kernel based approaches such as generalized discriminant analysis (GDA) has been successfully applied to extend LDA to nonlinear pattern recognition tasks. However, selecting an appropriate kernel function is usually difficult. Utilizing an implicit kernel mapping may face potential over-training problems for some complex and noised tasks. Our proposed method gives an alternative solution for nonlinear discriminant analysis while the conventional linear and nonlinear approaches are difficult to achieve a satisfactory results. Experiments on both synthetic data and face data set show the effectiveness of the proposed methods.