Abstract
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.
Highlights
Graph neural networks have been successfully applied to handling non-Euclidean data such as graph-structured data [1]
We propose a novel approach to appropriately define a large receptive field for Graph neural networks (GNNs) by incorporating high-order proximity information extracted from the input graph
First of all, inspired by a non-negative matrix factorization method that is trainable on neural network models [16], [17], we propose to design a group-aware and flexible receptive field for GNNs
Summary
Graph neural networks have been successfully applied to handling non-Euclidean data such as graph-structured data (e.g. social networks, 3D point clouds, and biological networks) [1]. Taking Scenario 2 as an example, with the increased receptive field, the bridge node can better perceive the topological structure embedded in the graph (without leveraging the label information) and adjust its local aggregation process In this case, high-order proximity information provides topology-aware aggregation and can suppress the noise from the green group. We will further demonstrate the benefit of incorporating high-order proximity information for aggregation on real-world datasets (see Fig. for details) Another known issue in graph convolution related framework is that convolving all connected neighbors of a node without considering their topological roles does not comply with a basic but widely accepted hypothesis in graph analysis – different neighbors contribute differently to the VOLUME 7, 2019 node. 3) We conduct extensive experiments and analysis to demonstrate the effectiveness of hpGAT on several real-world datasets. hpGAT outperforms the state-ofthe-art methods, and its superior performance is corroborated by observing its boosted performance in classifying nodes connecting to different groups
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