Semi-supervised multi-label feature selection with consistent sparse graph learning

In practical domains, high-dimensional data are usually associated with diverse semantic labels, whereas traditional feature selection methods are designed for single-label data. Moreover, existing multi-label methods encounter two main challenges in semi-supervised scenarios: (i). Most semi-supervised methods fail to evaluate the label correlations without enough labeled samples, which are the critical information of multi-label feature selection, making label-specific features discarded. (ii). The similarity graph structure directly derived from the original feature space is suboptimal for multi-label problems in existing graph-based methods, leading to unreliable soft labels and degraded feature selection performance. To overcome them, we propose a consistent sparse graph learning method for multi-label semi-supervised feature selection (SGMFS), which can enhance the feature selection performance by maintaining space consistency and learning label correlations in semi-supervised scenarios. Specifically, for Challenge (i), SGMFS learns a low-dimensional and independent label subspace from the projected features, which can compatibly cross multiple labels and effectively achieve the label correlations. For Challenge (ii), instead of constructing a fixed similarity graph for semi-supervised learning, SGMFS thoroughly explores the intrinsic structure of the data by performing sparse reconstruction of samples in both the label space and the learned subspace simultaneously. In this way, the similarity graph can be adaptively learned to maintain the consistency between the label space and the learned subspace, which can promote propagating proper soft labels for unlabeled samples, facilitating the ultimate feature selection. An effective solution with fast convergence is designed to optimize the objective function. Extensive experiments validate the superiority of SGMFS.