Two-Dimensional Principal Component Analysis (2D-PCA) is one of the most simple and effective feature extraction methods in the field of pattern recognition. However, the traditional 2D-PCA lacks robustness and the function of sparse feature extraction. In this paper, we propose a new feature extraction approach based on the traditional 2D-PCA, which is called Nuclear Norm Based Two-Dimensional Sparse Principal Component Analysis (N-2D-SPCA). To improve the robustness of 2D-PCA, we utilize nuclear norm to measure the reconstruction error of loss function. At the same time, we obtain sparse feature extraction by adding [Formula: see text]-norm and [Formula: see text]-norm regularization terms to the model. By designing an alternatively iterative algorithm, we can solve the optimization problem and learn a projection matrix for use with feature extraction. Besides, we present a bilateral projections model (BN-2D-SPCA) to further compress the dimensions of the feature matrix. We verify the effectiveness of our method on four benchmark face databases including AR, ORL, FERET and Yale databases. Experimental results show that the proposed method is more robust than some state-of-the-art methods and the traditional 2D-PCA.
