Interpretable Multi-View Feature Representation via Physical Partial Differential Equation

Graph Neural Networks (GNNs) have become a powerful tool for learning representations from graph-structured data, leveraging the relationships between nodes and their features. Despite their success, they often lack interpretability due to the black-box nature of neural networks, and further development may be limited. Moreover, previous GNN-based multi-view methods typically rely on simple feature fusion techniques such as weighted averaging or concatenation, which fail to capture the complex dependencies between views. In this paper, we propose a novel framework, namely Interpretable Multi-View Feature Representation via physical partial differential equation (IMvFR), to address these limitations in the context of multi-view semi-supervised learning. By integrating GNNs with partial differential equations (PDEs), we model the evolution of multi-view feature representations as a dynamic process. This provides a natural and interpretable framework for understanding how information flows between different views, overcoming the black-box nature of traditional GNNs. Additionally, we formulate multi-view feature representations as an initial-value problem within the framework of PDEs, providing a clear and interpretable mechanism for label propagation and feature fusion, thus facilitating the acquisition of global and local information between views. Comprehensive experimental results on eight datasets demonstrate that the proposed method achieves superior performance compared with state-of-the-art methods.