Semi-supervised multi-label feature selection with local logic information preserved

In reality, like single-label data, multi-label data sets have the problem that only some have labels. This is an excellent challenge for multi-label feature selection. This paper combines the logistic regression model with graph regularization and sparse regularization to form a joint framework (SMLFS) for semi-supervised multi-label feature selection. First of all, the regularization of the feature graph is used to explore the geometry structure of the feature, to obtain a better regression coefficient matrix, which reflects the importance of the feature. Second, the label graph regularization is used to extract the available label information, and constrain the regression coefficient matrix, so that the regression coefficient matrix can better fit the label information. Third, the \(L_{2,p}\)-norm \(0<p\le 1\) constraint is used to ensure the sparsity of the regression coefficient matrix so that it is more convenient to distinguish the importance of features. In addition, an iterative updating algorithm with convergence is designed and proved to solve the above problems. Finally, the proposed method is validated on eight classic multi-label data sets, and the experimental results show the effectiveness of the proposed algorithm.