Scalable Multi-view Unsupervised Feature Selection with Structure Learning and Fusion

To tackle the high-dimensional data with multiple representations, multi-view unsupervised feature selection has emerged as a significant learning paradigm. However, previous methods suffer from the following dilemmas: (i) They focus on selecting the features that preserve the similarity structure of data, whereas neglecting the discriminative information in the cluster structure; (ii) The orthogonal constraint is often imposed on the pseudo cluster labels, breaking the locality in the cluster label space; (iii) Learning the similarity or cluster structure from all samples is time-consuming. To this end, a Scalable Multi-view Unsupervised Feature Selection with structure learning and fusion (SMUFS) is proposed to jointly exploit the cluster structure and the similarity relations of data. Specifically, SMUFS introduces the sample-view weights to adaptively fuse the membership matrices that indicate cluster structures and serve as the pseudo cluster labels, such that a unified membership matrix across views can be effectively obtained to guide feature selection. Meanwhile, SMUFS performs graph learning from the membership matrix, preserving the locality of cluster labels and improving their discriminative capability. Further, an acceleration strategy has been developed to make SMUFS scalable for large-scale data. An iterative optimization is designed to solve the formulated objective function, and extensive experiments demonstrate the superiority of SMUFS.