Bilinear matrix regression based on matrix data can directly select the features from matrix data by deploying several couples of left and right regression matrices. However, the existing matrix regression methods do not consider the local geometric structure of the samples, which results in poor classification performance. This study proposes a robust graph regularised sparse matrix regression method for two-dimensional supervised feature selection, where the intra-class compactness graph based on the manifold learning is used as the regularisation item, and the -norm as loss functions to establish the authors’ matrix regression model. An alternating optimisation algorithm is also devised to solve it and give its closed-form solutions in each iteration. The proposed method not only can learn the left and right regression matrices, but also can preserve the intrinsic geometry structure by using the label information. Extensive experiments on several data sets demonstrate the superiority of the proposed method.

中文翻译：

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用于二维监督特征选择的鲁棒图正则化稀疏矩阵回归

通过部署几对左右回归矩阵，基于矩阵数据的双线性矩阵回归可以直接从矩阵数据中选择特征。但是，现有的矩阵回归方法没有考虑样本的局部几何结构，这导致分类性能较差。这项研究提出了一种鲁棒的图正则化稀疏矩阵回归方法用于二维监督特征选择，其中基于流形学习的类内紧实度图被用作正则化项，并且 -norm作为损失函数来建立作者的矩阵回归模型。还设计了一种交替优化算法来求解它，并在每次迭代中给出其闭式解。所提出的方法不仅可以学习左右回归矩阵，而且可以通过使用标签信息保留固有的几何结构。在几个数据集上的大量实验证明了该方法的优越性。