Matrix regression (MR) is a regression model that can directly perform on matrix data. However, the effect of each element in matrix data on regression model is different. Taking into consideration the relevance of every original feature in the matrix data and their influence on the final estimation of the regression model, we introduce an unknown weight matrix to encode the relevance of feature in matrix data and propose a feature weighting and graph-based matrix regression (FWGMR) model for image supervised feature selection. In this model, the feature weight matrix is used to select some important features from the matrix data and preserve the relative spatial location relationship of elements in the matrix data. In addition, in order to effectively and reasonably preserve the local manifold structure of the training matrix samples, a regularization term in the model is used to adaptively learn a graph matrix on low-dimensional space. An optimization algorithm is devised to solve FWGMR model and to provide the closed-form solutions of this model in each iteration. Extensive experiments on some public datasets demonstrate the superiority of FWGMR.

矩阵回归（MR）是可以直接对矩阵数据执行的回归模型。但是，矩阵数据中每个元素对回归模型的影响是不同的。考虑到矩阵数据中每个原始特征的相关性及其对回归模型最终估计的影响，我们引入了未知权重矩阵对矩阵数据中特征的相关性进行编码，并提出了特征加权和基于图的矩阵回归（FWGMR）模型用于图像监督特征选择。在该模型中，特征权重矩阵用于从矩阵数据中选择一些重要特征，并保留矩阵数据中元素的相对空间位置关系。另外，为了有效合理地保留训练矩阵样本的局部流形结构，模型中的正则化项用于自适应地学习低维空间上的图矩阵。设计了一种优化算法来求解FWGMR模型，并在每次迭代中提供该模型的封闭形式解决方案。在一些公共数据集上的大量实验证明了FWGMR的优越性。