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 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

Capped norm linear discriminant analysis and its applications

Classical linear discriminant analysis (LDA) is based on squared Frobenious norm and hence is sensitive to outliers and noise. To improve the robustness of LDA, in this paper, we introduce capped l_{2,1}-norm of a matrix, which employs non-squared l_2-norm and "capped" operation, and further propose a novel capped l_{2,1}-norm linear discriminant analysis, called CLDA. Due to the use of capped l_{2,1}-norm, CLDA can effectively remove extreme outliers and suppress the effect of noise data. In fact, CLDA can be also viewed as a weighted LDA. CLDA is solved through a series of generalized eigenvalue problems with theoretical convergency. The experimental results on an artificial data set, some UCI data sets and two image data sets demonstrate the effectiveness of CLDA