Max-Min Robust Unsupervised Feature Selection via Sparse Subspace

Feature selection is one of the hot issues in machine learning. It reduces storage pressure by effectively screening features and has become a very practical data preprocessing method. At present, most feature selection algorithms apply $\ell _{2,1}$ -norm on the transformation matrix to calculate the scores for all features and then select appropriate features according to these scores. But their sparsity is limited, and meaningless regularization parameters increase the cost, making it prone to falling into local optimum. To solve the above difficulties, this article proposes a novel max-min robust unsupervised feature selection via sparse subspace (MMRUFS), which considers both the reconstruction term and variance term of data, so that the model can not only fully retain the original information of data, but also make the data more dispersed. Second, $\ell _{2,0}$ -norm constraint is used on the transformation matrix to directly select the optimal feature subset, avoiding the fine-tuning of regularization parameters. To enhance the robustness, MMRUFS carefully designs mark weight vector to make the model treat normal samples and outliers differently and achieves the effect of anomaly detection. Finally, MMRUFS is solved by designing the surrogate matrix, and its convergence is strictly guaranteed, experimental results reveal that MMRUFS outperforms other feature selection algorithms on multiple real-world datasets.