In this paper, we propose an L1-norm two-dimensional linear discriminant analysis (L1-2DLDA) with robust performance. Different from the conventional two-dimensional linear discriminant analysis with L2-norm (L2-2DLDA), where the optimization problem is transferred to a generalized eigenvalue problem, the optimization problem in our L1-2DLDA is solved by a simple justifiable iterative technique, and its convergence is guaranteed. Compared with L2-2DLDA, our L1-2DLDA is more robust to outliers and noises since the L1-norm is used. This is supported by our preliminary experiments on toy example and face datasets, which show the improvement of our L1-2DLDA over L2-2DLDA.
Li, C. N., Shao, Y. H., & Deng, N. Y. (2015). Robust L1-norm two-dimensional linear discriminant analysis. Neural Networks, 65, 92–104. https://doi.org/10.1016/j.neunet.2015.01.003