Where Views Meet Curves: Virtual Anchors for Hyperbolic Multi-View Graph Diffusion

摘要

In recent years, graph-based multi-view learning has received widespread attention for its ability to utilize data dependencies to capture more comprehensive information from ubiquitous multi-view data. However, with the increase in data size and complexity, Euclidean space struggles to capture the hierarchical and exponentially expanding relationships of multi-view data in limited dimensions, leading to embedding distortion and insufficient cross-view alignment and interaction. To this end, we propose a hyperbolic multi-view heat diffusion method. Firstly, we utilize the negative curvature advantage of the hyperbolic space to construct a graph representation for each view separately, so that each view can still retain its hierarchical structure in relatively low dimensions. Then we construct a graph heat diffusion process on hyperbolic manifolds to ensure that each view is locally smoothed and globally aggregated while achieving semantic consistency through virtual views. We show that the method can be interpreted as a Riemannian gradient descent process for collaborative learning on hyperbolic manifolds, which not only effectively fuses multimodal information, but also significantly enhances the interaction and unified representation among different views. Experimental results show that the proposed framework achieves excellent performance in a variety of multi-view scenarios.