Structure-aware Hybrid-order Similarity Learning for Multi-view Unsupervised Feature Selection

Multi-view unsupervised feature selection (MUFS) has recently emerged as an effective dimensionality reduction method for unlabeled multi-view data. However, most existing methods mainly use first-order similarity graphs to preserve local structure, often overlooking the global structure that can be captured by second-order similarity. In addition, a few MUFS methods leverage predefined second-order similarity graphs, making them vulnerable to noise and outliers and resulting in suboptimal feature selection performance. In this paper, we propose a novel MUFS method, termed Structure-aware Hybrid-order sImilarity learNing for multi-viEw unsupervised Feature Selection (SHINE-FS), to address the aforementioned problem. SHINE-FS first learns consensus anchors and the corresponding anchor graph to capture the cross-view relationships between the anchors and the samples. Based on the acquired cross-view consensus information, it generates low-dimensional representations of the samples, which facilitate the reconstruction of multi-view data by identifying discriminative features. Subsequently, it employs the anchor-sample relationships to learn a second-order similarity graph. Furthermore, by jointly learning first-order and second-order similarity graphs, SHINE-FS constructs a hybrid-order similarity graph that captures both local and global structures, thereby revealing the intrinsic data structure to enhance feature selection. Comprehensive experimental results on real multi-view datasets show that SHINE-FS outperforms the state-of-the-art methods.