Structural Node Representation on Irregular Roles

Abstract

Roles of nodes refer to the structural patterns of relations that reflect node identities or functions in the graph or network. Learning role-based node representations has been a hot topic in the last decade, as they are helpful in fully understanding the internal mechanisms of the network and improving performance on downstream tasks. In real-world networks, the dependencies between the roles are extremely complex, where the local structures of nodes can vary considerably even if they share the same role. However, existing methods ignore the varying dependencies and fail to discover roles with an irregular structure. To fully understand the above problems, we first propose an index based on a graph kernel to measure role irregularity and analyze its influence on downstream tasks. Then, for practically overcoming the shortcomings, we propose a novel framework based on a graph neural network and a variational auto-encoder with a cross-attention mechanism (GVCAM). It leverages the graph convolutional network to preserve the varying dependencies between nodes and the variational auto-encoder to capture the structural traits of nodes. We introduce the cross-attention mechanism that fuses the two parts to adaptively learn the irregular roles. Extensive experiments on one synthetic and six real-world datasets show that GVCAM achieves competitive performance across multiple tasks compared with ten state-of-the-art baselines.