Feature selection is able to select more discriminative features for classification and plays an important role in multi-label learning to alleviate the effect of the curse of dimensionality. Recently, the multi-label feature selection methods based on the sparse regression model have received increasing attentions. However, most of these methods directly project original data space to label space in the regression model, which is inappropriate because the linear assumption between data space and label space doesn't hold in most cases. In the paper, we propose a feature selection method named multi-label feature selection via manifold regularization and dependence maximization (MRDM). In the regression model of MRDM, the original data space is projected to a low-dimensional manifold space, which not only has the same topological structure with the original data, but also has a strong dependence with the class labels. Then, an objective function involving $l_{2,1}$-norm regularization is formulated, and an alternating optimization-based iterative algorithm is designed to obtain the sparse coefficients for multi-label feature selection. Extensive experiments on various multi-label data sets demonstrate the superiority of the proposed method compared with some state-of-the-art multi-label feature selection methods.

特征选择能够选择更具判别性的特征进行分类，在多标签学习中发挥重要作用，减轻维数灾难的影响。近年来，基于稀疏回归模型的多标签特征选择方法受到越来越多的关注。然而，这些方法大多直接将原始数据空间投影到回归模型中的标签空间，这是不合适的，因为数据空间和标签空间之间的线性假设在大多数情况下不成立。在本文中，我们提出了一种通过流形正则化和依赖最大化（MRDM）的特征选择方法，称为多标签特征选择。在MRDM的回归模型中，将原始数据空间投影到低维流形空间，它不仅与原始数据具有相同的拓扑结构，而且与类标签具有很强的依赖性。那么，一个目标函数涉及${升}_{2,1}$-norm 正则化被公式化，并设计了一种基于交替优化的迭代算法来获得用于多标签特征选择的稀疏系数。与一些最先进的多标签特征选择方法相比，对各种多标签数据集的大量实验证明了所提出的方法的优越性。