${R}_1$ -2-DPCA and Face Recognition

2-D principal component analysis (2-DPCA) is one of the successful dimensionality reduction approaches for image classification and representation. However, 2-DPCA is not robust to outliers. To tackle this problem, we present an efficient robust method, namely ${R} _{1}$ -2-DPCA for feature extraction. ${R} _{1}$ -2-DPCA aims to seek the projection matrix such that the projected data have the maximum variance, which is measured by ${R} _{1}$ -norm. Compared with most existing robust 2-DPCA methods, our model is not only robust to outliers but also helps encode discriminant information. Accordingly, we develop a nongreedy iterative algorithm, which has not only a closed-form solution in each iteration but also a good convergence, to solve our model. Moreover, to further improve classification performance, we employ nuclear norm as the distance metric in the classification phase. Extensive experiments on several face databases illustrate that our proposed method is superior to most existing robust 2-DPCA methods.