Revisiting graph neural networks from hybrid regularized graph signal reconstruction

Area of Science:

• Artificial Intelligence
• Machine Learning
• Graph Neural Networks

Background:

• Graph Neural Networks (GNNs) excel at processing graph-structured data but lack a systematic development approach and unified theoretical foundation.
• Existing GNN models often rely on message-passing mechanisms, making it difficult to explain their design concepts cohesively.

Purpose of the Study:

• To present a unified optimization framework for GNNs based on hybrid regularized graph signal reconstruction.
• To establish a theoretical connection between aggregation operations in different GNN models.
• To guide the development of novel GNN architectures.

Main Methods:

• Developed a unified optimization framework linking GNN aggregation to graph signal reconstruction.
• Mathematically explained classic GNN models within the new framework.
• Designed a GNN model (GNN-MD) using model-driven (fixed-point iteration) and data-driven (dictionary learning) approaches.
• Theoretically analyzed the convergence of the proposed GNN-MD model.

Main Results:

• The unified framework reveals that GNN information aggregation is an optimization process.
• Classic GNN models are explained and compared from a macro perspective.
• The GNN-MD model demonstrates excellent performance in node classification tasks.
• GNN-MD outperforms baseline models, especially on datasets with high-dimensional features.

Conclusions:

• The proposed framework offers a convenient way to understand GNNs and guides the design of new models.
• The GNN-MD model represents a significant advancement in GNN architectures.
• The findings have implications for advancing research in graph representation learning and its applications.