  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 the sensitivity 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 the robustness. The other one is that by
introducing an extra regularization term, G2DLDA achieves better generalization
performance, and solves the singularity problem. In addition, G2DLDA can be
solved through a series of convex problems with equality constraint, and it has
closed solution for each single problem. Its convergence can be guaranteed
theoretically when $1\leq p\leq2$. Preliminary experimental results on three
contaminated human face databases show the effectiveness of the proposed
G2DLDA.
