Bilinear analysis for kernel selection and nonlinear feature extraction

This paper presents a unified criterion, Fisher + kernel criterion (FKC), for feature extraction and recognition. This new criterion is intended to extract the most discriminant features in different nonlinear spaces, and then, fuse these features under a unified measurement. Thus, FKC can simultaneously achieve nonlinear discriminant analysis and kernel selection. In addition, we present an efficient algorithm Fisher + kernel analysis (FKA), which utilizes the bilinear analysis, to optimize the new criterion. This FKA algorithm can alleviate the ill-posed problem existed in traditional kernel discriminant analysis (KDA), and usually, has no singularity problem. The effectiveness of our proposed algorithm is validated by a series of face-recognition experiments on several different databases. Index Terms--Bilinear analysis, discriminant analysis, face recognition, feature extraction, Fisher criterion, kernel selection.