Low-rank structure preserving for unsupervised feature selection

Unsupervised feature selection has been widely applied to machine learning and pattern recognition, as it does not require class labels. The majority of the popular unsupervised feature selection methods focus on various forms of reconstruction, and minimize the reconstruction residual by discarding features with low contributions. However, they cannot effectively preserve the data distribution in multiple subspaces, because the sample structure information is not substantially utilized to constrain the selected features. In this paper, we propose a low-rank structure preserving method for unsupervised feature selection (LRPFS) to address this shortcoming. The data matrix consisting selected features is assumed as a dictionary, which is learned by a low-rank constraint to preserve the subspace structure. Meanwhile, we further leverage the sparse penalty to remove the redundancy features, and thus obtain the discriminative features with intrinsic structures. In this way, the sample distribution can be preserved by low-rank constraint more precisely via using discriminative features. In turn, the refined sample structure boosts the selection of more representative features. The effectiveness of our method is supported by both theoretical and experimental results.