Bilinear Analysis for Kernel Selection and Nonlinear Feature Extraction

Shu Yang, Shuicheng YAN, Chao Zhang, Xiaoou Tang

Abstract: para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a unified criterion, Fisher <formula formulatype="inline"> <tex>${+}$</tex></formula> 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 <formula formulatype="inline"><tex>${+}$</tex></formula> 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. </para>