Contents 1. Introduction
Face recognition is a highly complex and nonlinear problem because there exists so many image variations such as pose, illumination and facial expression [10]. These variations would give a nonlinear distribution of face images of an individual. In turn linear methods, such as linear discriminant analysis (LDA) [3], [4] could not provide sufficient nonlinear discriminant power to handle the problem. To overcome this limitation, Kernel approach has been proposed [5]. Follows the success of applying kernel trick in SVM, a lot of Kernel-based recognition algorithms have been developed to solve nonlinear problems in face recognition such as Kernel Fisher discriminant (KFD) [2], [7], kernel principle component analysis (KPCA) [6]. It is also shown that kernel-based approach is a feasible approach to solve the nonlinear problems in face recognition. However, there are a number of open questions that we need to solve such as the selection of kernel functions and selection of kernel parameters. This paper mainly focuses on the selection of kernel parameters. We select the “universal kernel” in this paper, in which there are a number of scale factors as follows, $$K(x,y)=\exp\left(-\sum\limits_{i}{(x_{i}-y_{i})^{2}\over 2\theta_{i}^{2}}\right)\eqno{\hbox{(1)}}$$
