Robust jointly sparse regression for image feature selection

In this paper, we proposed a novel model called Robust Jointly Sparse Regression (RJSR) for image feature selection. In the proposed model, the L21-norm based loss function is robust to outliers and the L21-norm regularization term guarantees the joint sparsity for feature selection. In addition, the model can solve the small-class problem in the regression-based methods or the LDA-based methods. Comparing with the traditional L21-norm minimization based methods, the proposed method is more robust to noise since the flexible factor and the robust measurement are incorporated into the model to perform feature extraction and selection. An alternatively iterative algorithm is designed to compute the optimal solution. Experimental evaluation on several well-known data sets shows the merits of the proposed method on feature selection and classification, especially in the case when the face image is corrupted by block noise.