Generalized two-dimensional linear discriminant analysis with regularization.

Recent advances show that two-dimensional linear discriminant analysis (2DLDA) is a successful matrix based dimensionality reduction method. However, 2DLDA may encounter the singularity issue theoretically, and also is sensitive to outliers. In this paper, a generalized Lp-norm 2DLDA framework with regularization for an arbitrary p>0 is proposed, named G2DLDA. There are mainly two contributions of G2DLDA: one is G2DLDA model uses an arbitrary Lp-norm to measure the between-class and within-class scatter, and hence a proper p can be selected to achieve robustness. The other one is that the introduced regularization term makes G2DLDA enjoy better generalization performance and avoid singularity. In addition, an effective learning algorithm is designed for G2LDA, which can be solved through a series of convex problems with closed-form solutions. Its convergence can be guaranteed theoretically when 1≤p≤2. Preliminary experimental results on three contaminated human face databases show the effectiveness of the proposed G2DLDA.