Multi-label feature selection via robust flexible sparse regularization

Multi-label feature selection is an efficient technique to deal with the high dimensional multi-label data by selecting the optimal feature subset. Existing researches have demonstrated that l1-norm and l2,1-norm are promising roles for multi-label feature selection. However, two important issues are ignored when existing l1-norm and l2,1-norm based methods select discriminative features for multi-label data. First, l1-norm can enforce sparsity on each feature across all instances while numerous selected features lack discrimination due to the generated zero weight values. Second, l2,1-norm not only neglects label-specific features but also ignores the redundancy among features. To this end, we design a Robust Flexible Sparse Regularization norm (RFSR), furthermore, proposing a global optimization framework named Robust Flexible Sparse regularized multi-label Feature Selection (RFSFS) based on RFSR. Finally, an efficient alternating multipliers based optimization scheme is developed to iteratively optimize RFSFS. Empirical studies on fifteen benchmark multi-label data sets demonstrate the effectiveness and efficiency of RFSFS.