Linear Complexity Multi-View Unsupervised Feature Selection via Anchor-Based Feature Relationship Construction

In recent years, multi-view unsupervised feature selection has gained significant interest for its ability to efficiently handle multi-view datasets while offering better interpretability. Existing multi-view unsupervised feature selection methods construct graphs based on the relationship between samples. In fact, in feature selection, it is more important to focus on the relationships between features. However, constructing a complete graph to capture the relationship between features would incur a space and time complexity of $O(d^{2})$ or even higher. Therefore, we introduce an anchor-based strategy and build a feature bipartite graph to reduce complexity. In addition, since existing methods cannot directly extract feature importance from a feature bipartite graph, we design an effective and low-complexity method to directly obtain feature scores from a feature bipartite graph. Compared with the feature importance extraction method based on the complete graph, our proposed method reduces the time complexity from $O(d^{3})$ to $O(d)$ . To the best of our knowledge, our proposed method is the first multi-view unsupervised feature selection algorithm that achieves $O(nd)$ space and time complexity without data segmentation. Specifically, this method adaptively learns feature-level anchor graph structures through self-expressive multi-view subspace learning, which can effectively capture the structural information between features and anchors. Meanwhile, the proposed method projects low-dimensional anchors to common dimensions and aligns them with consensus anchors to capture the consistency and complementary information between different views. The superiority of the proposed algorithm is demonstrated by comparing it with seven state-of-the-art algorithms on five public image and two biological information multi-view datasets. The code of the proposed method is publicly available at https://github.com/getupLiu/AFRC.