Unsupervised multi-view feature selection via attentive hierarchical bipartite graphs with optimizable graph filter

Unsupervised multi-view feature selection is crucial for tackling high-dimensional data from multiple sources, with broad applications. However, bipartite graph-based methods face three key limitations: (1) Graph construction struggles to determine optimal anchor numbers, and using a fixed number fails to capture multi-scale hierarchical and non-linear structures; (2) Graph fusion lacks adaptive weighting across both hierarchies and views, restricting consensus graph learning; (3) Feature selection overlooks the impact of redundant spectral components in the graph's frequency domain on discriminative feature evaluation. These limitations collectively hinder graph quality and feature selection performance. We address these limitations with a novel approach: First, we propose an efficient, parameter-free method for constructing multi-view hierarchical bipartite graphs. This method links samples from parent clusters to their child cluster centroids at various scales using hierarchical agglomerative clustering with nearest neighbor relations. Second, we present an attentive fusion strategy. It features truncated hierarchy selection and implicit hierarchy weighting to adaptively select and weight multi-view multi-hierarchical graphs for consensus structured graph learning. Finally, we incorporate an optimizable graph filter to find a low-dimensional representation. This representation is encoded by the filter, a row-wise sparse projection, and the feature matrix, and decoded to reconstruct the consensus graph while maximizing data variance. An alternating iterative algorithm is designed to optimize our model, supported by theoretical analysis from different perspectives. Extensive experiments on 8 real-world datasets demonstrate significant improvements with our approach over 15 state-of-the-art methods, including a 12.77% ACC increase on the Caltech101-20 dataset. The code and datasets are available on GitHub: https://github.com/xiadongcs/HBGOF.