Discriminant Analysis via Joint Euler Transform and l_2,1-Norm

Linear discriminant analysis (LDA) has been widely used for face recognition. However, when identifying faces in the wild, the existence of outliers that deviate significantly from the rest of the data can arbitrarily skew the desired solution. This usually deteriorates LDA's performance dramatically, thus preventing it from mass deployment in real-world applications. To handle this problem, we propose an effective distance metric learning method-based LDA, namely, Euler LDA-L21 (e-LDA-L21). e-LDA-L21 is carried out in two stages, in which each image is mapped into a complex space by Euler transform in the first stage and the l_2,1-norm is adopted as the distance metric in the second stage. This not only reveals nonlinear features but also exploits the geometric structure of data. To solve e-LDA-L21 efficiently, we propose an iterative algorithm, which is a closed-form solution at each iteration with convergence guaranteed. Finally, we extend e-LDA-L21 to Euler 2DLDA-L21 (e-2DLDA-L21) which further exploits the spatial information embedded in image pixels. Experimental results on several face databases demonstrate its superiority over the state-of-the-art algorithms.