Improve noise tolerance of robust feature selection via block-sparse projection learning

Feature selection (FS) is crucial in robust representation learning by identifying informative features within high-dimensional data. However, the presence of noise can lead to the misidentification of features and distort data representation. Existing robust feature selection algorithms typically discard noisy features, leading to the loss of potentially beneficial information. Additionally, these methods are often hindered by the difficulty of tuning sparse regularization parameters, further affecting generalization. To address this, we propose a method for improving the noise tolerance of robust feature selection (NTRFS), which actively identifies and exploits beneficial noise during the selection process to enhance robustness. Specifically, NTRFS incorporates block-sparse projection learning with ${\ell }_{2,1}$-norm minimization, enhancing the model’s robustness to noise while preserving key features by leveraging the informative aspects of noise. Furthermore, by integrating anomaly estimation with adaptive weighting, NTRFS utilizes noise-tolerant information to promote the discovery of class prototypes, adjusting the weight of each feature based on its informative saliency. Additionally, the proposed ${\ell }_{2,0}$-norm constrained block-sparse projection learning module enhances discriminative power by exploiting local geometric relationships in data manifolds, without requiring regularization parameter tuning. Finally, to tackle the non-convex trace ratio and NP-hard block sparsity problems, we propose an efficient iterative optimization algorithm with guaranteed convergence. Experimental results on several real-world datasets show that NTRFS enhances robustness and improves classification performance by leveraging noise, outperforming advanced robust FS methods.