Discriminative feature grouping

Feature grouping has been demonstrated to be promising in learning with high-dimensional data. It helps reduce the variances in the estimation and improves the stability of feature selection. One major limitation of existing feature grouping approaches is that some similar but different feature groups are often mis-fused, leading to impaired performance. In this paper, we propose a Discriminative Feature Grouping (DFG) method to discover the feature groups with enhanced discrimination. Different from existing methods, DFG adopts a novel regularizer for the feature coefficients to tradeoff between fusing and discriminating feature groups. The proposed regularizer consists of a l ₁ norm to enforce feature sparsity and a pairwise l∞ norm to encourage the absolute differences among any three feature coefficients to be similar. To achieve better asymptotic property, we generalize the proposed regularizer to an adaptive one where the feature coefficients are weighted based on the solution of some estimator with root-n consistency. For optimization, we employ the alternating direction method of multipliers to solve the proposed methods efficiently. Experimental results on synthetic and real-world datasets demonstrate that the proposed methods have good performance compared with the state-of-the-art feature grouping methods.