Kernel-based Weighted Discriminant Analysis with QR Decomposition and Its Application to Face Recognition

Kernel discriminant analysis (KDA) is a widely used approach in feature extraction problems. However, for high-dimensional multi-class tasks, such as faces recognition, traditional KDA algorithms have a limitation that the Fisher criterion is non-optimal with respect to classification rate. Moreover, they suffer from the small sample size problem. This paper presents two variants of KDA called based on QR decomposition weighted kernel discriminant analysis (WKDA/QR), which can effectively deal with the above two problems, and based on singular value decomposition weighted kernel discriminant analysis (WKDA/SVD). Since the QR decomposition on a small size matrix is adopted, the superiority of the proposed method is its computational efficiency and can avoid the singularity problem. In addition, we compare WKDA/QR with WKDA/SVD under the parameters of weighted function and kernel function. Experimental results on face recognition show that the WKDA/QR and WKDA/SVD are more effective than KDA, and WKDA/QR is more effective and feasible than WKDA/SVD. Key–Words: QR decomposition, Kernel discriminant analysis (KDA), Feature extraction, Face recognition, small sample size (SSS)