Multi-label learning is usually used to mine the correlation between features and labels, and feature selection can retain as much information as possible through a small number of features. $\ell_{2,1}$ regularization method can get sparse coefficient matrix, but it can not solve multicollinearity problem effectively. The model proposed in this paper can obtain the most relevant few features by solving the joint constrained optimization problems of $\ell_{2,1}$ and $\ell_{F}$ regularization.In manifold regularization, we implement random walk strategy based on joint information matrix, and get a highly robust neighborhood graph.In addition, we given the algorithm for solving the model and proved its convergence.Comparative experiments on real-world data sets show that the proposed method outperforms other methods.

翻译：多标签学习通常用于挖掘特征与标签之间的相关性，而特征选择可以通过少量特征保留尽可能多的信息。$\ell_{2,1}$正则化方法能够获得稀疏系数矩阵，但无法有效解决多重共线性问题。本文提出的模型通过求解$\ell_{2,1}$与$\ell_{F}$正则化的联合约束优化问题，可获取最具相关性的少量特征。在流形正则化方面，我们基于联合信息矩阵实施随机游走策略，构建了具有高度鲁棒性的邻域图。此外，我们给出了该模型的求解算法并证明了其收敛性。在真实数据集上的对比实验表明，本文方法优于其他方法。