Adaptive Quasiconformal Kernel Fisher Discriminant Analysis via Weighted Maximum Margin Criterion

Kernel Fisher discriminant analysis (KFD) is an effective method to extract nonlinear discriminant features of input data using the kernel trick. However, conventional KFD algorithms endure the kernel selection problem as well as the singular problem. In order to overcome these limitations, a novel nonlinear feature extraction method called adaptive quasiconformal kernel Fisher discriminant analysis (AQKFD) via weighted maximum margin criterion (WMMC) is proposed in this paper. AQKFD, which solves the kernel selection problem, maps the data from the original input space into the quasiconformal kernel mapping space using a quasiconformal kernel. The adaptive parameters of the quasiconformal kernel are calculated through maximizing the measure of class separability of the input data in the quasiconformal kernel mapping space via WMMC which is in terms of the Fisher discriminant criterion. Moreover, when the weight parameter is approximate to the maximum value of Fisher discriminant criterion, then nonlinear features extracted by AQKFD-WMMC have the optimal class separability and AQKFD-WMMC can also solve the singular problem which is endured by KFD. Experimental results on the three real-world datasets, i.e., ORL, YALE and FERET face databases demonstrate the effectiveness of the proposed method.