Interpolatory Mercer kernel construction for kernel direct LDA on face recognition

This paper proposes a novel methodology on Mercer kernel construction using interpolatory strategy. Based on a given symmetric and positive semi-definite matrix (Gram matrix) and Cholesky decomposition, it first constructs a nonlinear mapping Phi, which is well-defined on the training data. This mapping is then extended to the whole input feature space by utilizing Lagrange interpolatory basis functions. The kernel function constructed by inner product is proven to be a Mercer kernel function. The self-constructed interpolatory Mercer (IM) kernel keeps the Gram matrix unchanged on the training samples. To evaluate the performance of the proposed IM kernel, a popular kernel direct linear discriminant analysis (KDDA) method for face recognition is selected. Comparing with RBF kernel based KDDA method on two face databases, namely FERET and CMU PIE databases, the IM kernel based KDDA approach could increase the performance by around 20% on CMU PIE database.