Multi-label learning is often used to mine the correlation between variables and multiple labels, and its research focuses on fully extracting the information between variables and labels. The $\ell_{2,1}$ regularization is often used to get a sparse coefficient matrix, but the problem of multicollinearity among variables cannot be effectively solved. In this paper, the proposed model can choose the most relevant variables by solving a joint constraint optimization problem using the $\ell_{2,1}$ regularization and Frobenius regularization. In manifold regularization, we carry out a random walk strategy based on the joint structure to construct a neighborhood graph, which is highly robust to outliers. In addition, we give an iterative algorithm of the proposed method and proved the convergence of this algorithm. The experiments on the real-world data sets also show that the comprehensive performance of our method is consistently better than the classical method.

翻译：多标签学习常常被用来挖掘变量和多个标签之间的相互关系,其研究的重点是充分提取变量和标签之间的信息。 $\ell\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\