Kernel-Based Nonlinear Discriminant Analysis for Face Recognition

Linear subspace analysis methods havebeen successfully applied to extract features for face recognition. Butthey are inadequate to represent the complex and nonlinear variations ofreal face images, such as illumination, facial expression and posevariations, because of their linear properties. In this paper, anonlinear subspace analysis method, Kernel-based Nonlinear DiscriminantAnalysis (KNDA), is presented for face recognition, which combines thenonlinear kernel trick with the linear subspace analysis method --- FisherLinear Discriminant Analysis (FLDA). First, the kernel trick is used toproject the input data into an implicit feature space, then FLDA isperformed in this feature space. Thus nonlinear discriminant featuresof the input data are yielded. In addition, in order to reduce thecomputational complexity, a geometry-based feature vectors selectionscheme is adopted. Another similar nonlinear subspace analysis isKernel-based Principal Component Analysis (KPCA), which combines thekernel trick with linear Principal Component Analysis (PCA). Experimentsare performed with the polynomial kernel, and KNDA is compared with KPCAand FLDA. Extensive experimental results show that KNDA can give ahigher recognition rate than KPCA and FLDA.