Multi-view feature selection via Nonnegative Structured Graph Learning

Abstract

Graph-based solutions have achieved state-of-the-art performance on unsupervised multi-view feature selection. However, existing methods generally characterize the sample similarities first by constructing multiple fixed graphs with manually determined parameters, and then perform the feature selection on a composite one. They will suffer from two severe problems: (1) The fixed graphs may be unreliable as the raw multi-view features usually contain adverse noises and cannot accurately capture the intrinsic sample relations. (2) The graph construction and feature selection are separate and independent, the two-step learning may lead to sub-optimal performance. To tackle these problems, in this paper, we propose an effective unsupervised multi-view feature selection method, dubbed as Nonnegative Structured Graph Learning (NSGL). Specifically, we develop a unified learning framework, which directly learns the structured graph from the raw features by imposing a rank constraint, and simultaneously performs adaptive feature selection with exploiting the complementarity of multi-view features. Besides, we introduce the pseudo label learning to extract the discriminative semantic information in unsupervised scenarios and steer the graph learning process. The informative features are finally selected by forcing the feature selection matrix to be sparse in rows with sparse regression. To solve the challenging optimization problem, we first transform the formulated problem into an equivalent one that can be tackled more easily, and then develop an efficient alternate optimization algorithm guaranteed with convergence to calculate the solution iteratively. Extensive experiments on several widely tested benchmarks demonstrate the superiority of NSGL compared with several state-of-the-art approaches.