Dual-graph with non-convex sparse regularization for multi-label feature selection

As for single-label learning, feature selection has become a crucial data pre-processing tool for multi-label learning due to its ability to reduce the feature dimensionality to mitigate the influence of "the curse of dimensionality". In recent years, the multi-label feature selection (MFS) methods based on manifold learning and sparse regression have confirmed their superiority and gained more and more attention than other methods. However, most of these methods only consider exploiting the geometric structure distributed in the data manifold but ignore the geometric structure distributed in the feature manifold, resulting in incomplete information about the learned manifold. Aiming to simultaneously exploit the geometric information of data and feature spaces for feature selection, this paper proposes a novel MFS method named dual-graph based multi-label feature selection (DGMFS). In the framework of DGMFS, two nearest neighbor graphs are constructed to form a dual-graph regularization to explore the geometric structures of both the data manifold and the feature manifold simultaneously. Then, we combined the dual-graph regularization with a non-convex sparse regularization l(2,1 - 2)-norm to obtain a more sparse solution for the weight matrix, which can better deal with the redundancy features. Finally, we adopt the EM strategy to design an iterative updating optimization algorithm for DGMFS and provide the convergence analysis of the optimization algorithm. Extensive experimental results on ten benchmark multi-label data sets have shown that DGMFS is more effective than several state-of-the-art MFS methods.