Adaptive unsupervised feature selection with robust graph regularization

Unsupervised feature selection, aiming at finding a refined representation of the original data by filtering out irrelevant and redundant features, has attracted intensive attention. Due to the dilemma of unavailable labels, existing methods select relevant features that preserve the intrinsic structure of data. Despite they are proven effective, the fixed metric is utilized to measure the distances from the projected samples to the target representation in the reconstruction term, which means that existing methods can not possess sufficient flexibility to adapt to different types of data sources. Besides, conventional methods utilize the l(2) norm based Laplacian graph to preserve the local structure of data, which leads to the sensitivity to noisy data. Inspired by the effectiveness and flexibility of the l(2,p) norm metric, we propose adaptive unsupervised feature selection with robust graph regularization (AUFS). Specifically, we impose the l(2,p) norm on the feature reconstruction term, which enhance the adaptability of our method to different types of data sources by adjusting p. In addition, l(2,1) norm based Laplacian graph is designed to alleviate the negative impact of noisy data. To solve the optimization problem, a unified iterative algorithm with guaranteed convergence is proposed. A large number of experimental results on several benchmark datasets demonstrate that our method outperforms some latest and related methods.