Two-dimensional jointly sparse robust discriminant regression

Ridge regression is an important method in feature extraction and has been extended in many different versions. Robust discriminant regression aims to solve the Small Sample Size Problem (SSSP) in ridge regression form by designing a novel regression model and imposing on L_2,1-norm as the main metric instead of the regularized term. However, when the dimensions of data are very high, RDR will be faced with the problem of the curse of dimensionality and high memory space cost. The computation cost of RDR will be extremely high in the iterative procedures. To address this problem, we propose an improved method called Two-dimensional jointly sparse RDR (2DJSRDR) for image-based feature extraction. Unlike previous vector-based methods which stretch the data into a high-dimensional vector as input, the proposed 2DJSRDR uses the two-dimensional image matrix directly as the computational unit so that the drawbacks in RDR can be naturally avoided. Besides, we also introduce L_2,1-norm as regularization term to obtain jointly sparse projections for feature selection, which is helpful to improve the performance of the model. Experiments on some benchmark datasets demonstrate the superior performance of the proposed method.