HpGAT: High-order proximity informed graph attention network

Graph neural networks (GNNs) have recently made remarkable breakthroughs in the paradigm of learning with graph-structured data. However, most existing GNNs limit the receptive field of the node on each layer to its connected (one-hop) neighbors, which disregards the fact that large receptive field has been proven to be a critical factor in state-of-the-art neural networks. In this paper, we propose a novel approach to appropriately define a variable receptive field for GNNs by incorporating high-order proximity information extracted from the hierarchical topological structure of the input graph. Specifically, multiscale groups obtained from trainable hierarchical semi-nonnegative matrix factorization are used for adjusting the weights when aggregating one-hop neighbors. Integrated with the graph attention mechanism on attributes of neighboring nodes, the learnable parameters within the process of aggregation are optimized in an end-to-end manner. Extensive experiments show that the proposed method (hpGAT) outperforms state-of-the-art methods and demonstrate the importance of exploiting high-order proximity in handling noisy information of local neighborhood.