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.

岭回归是特征提取中的一种重要方法，并在许多不同的版本中得到了扩展。鲁棒判别回归旨在通过设计新的回归模型并强加于岭回归形式来解决小样本量问题 (SSSP)${升}_{2,1}$-norm 作为主要指标而不是正则化项。但是，当数据的维数非常高时，RDR 会面临维数灾难和内存空间成本高的问题。在迭代过程中，RDR 的计算成本将非常高。为了解决这个问题，我们提出了一种改进的方法，称为二维联合稀疏 RDR (2DJSRDR)，用于基于图像的特征提取。与之前将数据拉伸为高维向量作为输入的基于向量的方法不同，所提出的 2DJSRDR 直接使用二维图像矩阵作为计算单元，因此可以自然地避免 RDR 的缺点。此外，我们还介绍${升}_{2,1}$-norm 作为正则化项，获得联合稀疏投影进行特征选择，有助于提高模型的性能。在一些基准数据集上的实验证明了所提出方法的优越性能。