Nuclear norm based two-dimensional sparse principal component analysis

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 L1-norm and L2-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 d...

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