Centrality Graph Shift Operators for Graph Neural Networks
This work addresses the need for more effective graph neural network operators in machine learning, particularly for tasks involving graph-structured data, though it is incremental as it builds on existing GSO frameworks.
The authors tackled the problem of improving graph representation learning by proposing Centrality Graph Shift Operators (CGSOs) that normalize adjacency matrices using global centrality metrics like PageRank, instead of traditional local degree-based methods, and demonstrated strong performance with a variant of Graph Convolutional Networks and Graph Attention Networks on real-world benchmark datasets, achieving competitive results.
Graph Shift Operators (GSOs), such as the adjacency and graph Laplacian matrices, play a fundamental role in graph theory and graph representation learning. Traditional GSOs are typically constructed by normalizing the adjacency matrix by the degree matrix, a local centrality metric. In this work, we instead propose and study Centrality GSOs (CGSOs), which normalize adjacency matrices by global centrality metrics such as the PageRank, $k$-core or count of fixed length walks. We study spectral properties of the CGSOs, allowing us to get an understanding of their action on graph signals. We confirm this understanding by defining and running the spectral clustering algorithm based on different CGSOs on several synthetic and real-world datasets. We furthermore outline how our CGSO can act as the message passing operator in any Graph Neural Network and in particular demonstrate strong performance of a variant of the Graph Convolutional Network and Graph Attention Network using our CGSOs on several real-world benchmark datasets.