Generalized two-dimensional linear discriminant analysis with regularization
This work addresses robustness and generalization problems in dimensionality reduction for face recognition, but it is incremental as it builds on existing 2DLDA methods.
The paper tackles the singularity and outlier sensitivity issues in two-dimensional linear discriminant analysis (2DLDA) by proposing a generalized Lp-norm framework with regularization, named G2DLDA, which achieves robustness and better generalization, as shown in preliminary experiments on three contaminated human face databases.
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.