Semi-supervised multi-view feature selection with adaptive similarity fusion and learning

Existing multi-view semi-supervised feature selection methods typically need to calculate the inversion of high-order dense matrices, rendering them impractical for large-scale applications. Meanwhile, traditional works construct similarity graphs on different views and directly fuse these graphs from the view level, ignoring the differences among samples in various views and the interplay between graph learning and feature selection. Consequently, both the reliability of graphs and the discrimination of selected features are compromised. To address these issues, we propose a novel multi-view semi-supervised feature selection with Adaptive Similarity Fusion and Learning (ASFL) for large-scale tasks. Specifically, ASFL constructs bipartite graphs for each view and then leverages the relationships between samples and anchors to align anchors and graphs across different views, preserving the complementarity and consistency among views. Moreover, an effective view-to-sample fusion manner is designed to coalesce the aligned graphs while simultaneously exploiting the neighbor structures in projection subspaces to construct the joint graph compatible across views, reducing the adverse effects of noisy features and outliers. By incorporating bipartite graph fusion and learning, label propagation, and $l_{2,0}$-norm multi-view feature selection into a unified framework, ASFL not only avoids the expensive computation in the solution procedures but also enhances the quality of selected features. An effective optimization strategy with fast convergence is developed to solve the objective function, and experimental results validate its efficiency and effectiveness over state-of-the-art methods.