Non-convex regularized self-representation for unsupervised feature selection

Feature selection aims to select a subset of features to decrease time complexity, reduce storage burden and improve the generalization ability of classification or clustering. For the countless unlabeled high dimensional data, unsupervised feature selection is effective in alleviating the curse of dimension-ality and can find applications in various fields. In this paper, we propose a non-convex regularized self-representation (RSR) model where features can be represented by a linear combination of other features, and propose to impose L_2,p norm (0 < p < 1) regularization on self-representation coefficients for unsupervised feature selection. Compared with the conventional L_{2, 1} norm regularization, when p < 1, much sparser solution is obtained on the self-representation coefficients, and it is also more effective in selecting salient features. To solve the non-convex RSR model, we further propose an efficient iterative reweighted least squares (IRLS) algorithm with guaranteed convergence to fixed point. Extensive experimental results on nine datasets show that our feature selection method with small p is more effective. It mostly outperforms features selected at p = 1 and other state-of-the-art unsupervised feature selection methods in terms of classification accuracy and clustering result.