Quadratic projection based feature extraction with its application to biometric recognition

•A novel quadratic projection based feature extraction framework is developed.•A set of quadratic matrices is learnt to distinguish each class from other classes.•Quadratic matrix learning (QML) is formulated as an SDP problem.•An efficient algorithm is developed to solve QML based on Lagrange duality theory.•Experiments on biometric recognition show the effectiveness of our algorithm.

This paper presents a novel quadratic projection based feature extraction framework, where a set of quadratic matrices is learned to distinguish each class from all other classes. We formulate quadratic matrix learning (QML) as a standard semidefinite programming (SDP) problem. However, the conventional interior-point SDP solvers do not scale well to the problem of QML for high-dimensional data. To solve the scalability of QML, we develop an efficient algorithm, termed DualQML, based on the Lagrange duality theory, to extract nonlinear features. To evaluate the feasibility and effectiveness of the proposed framework, we conduct extensive experiments on biometric recognition. Experimental results on three representative biometric recognition tasks, including face, palmprint, and ear recognition, demonstrate the superiority of the DualQML-based feature extraction algorithm compared to the current state-of-the-art algorithms.