Kernel Fisher Linear Discriminant with fractional power polynomial models for face recognition

This paper presents a kernel Fisher Linear Discriminant (FLD) method for face recognition. The kernel FLD method is extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semi-definite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semi-definite Gram matrix, either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. The feasibility of the kernel FLD method with fractional power polynomial models has been successfully tested on face recognition using a FERET data set that contains 600 frontal face images corresponding to 200 subjects. These images are acquired under variable illumination and facial expression. Experimental results show that the kernel FLD method with fractional power polynomial models achieves better face recognition performance than the Principal Component Analysis (PCA) method using various similarity measures, the FLD method, and the kernel FLD method with polynomial kernels.