Visiting Distant Neighbors in Graph Convolutional Networks

TL;DR

The paper addresses the limitation of first-neighbor aggregation in graph convolutional networks for semi-supervised node classification. It extends GCNs to higher-order neighborhoods by forming a linear combination of neighborhood-specific propagations with trainable coefficients, across distances from 0 to n, while using a shared weight matrix to keep parameter growth in check. Normalized adjacency representations for each neighborhood enable efficient, multi-hop aggregation without dense parameter increases. Empirical results on citation networks show improved accuracy over standard GCNs when labeled data are scarce, demonstrating the value of incorporating long-range structural information in graph representations.

Abstract

We extend the graph convolutional network method for deep learning on graph data to higher order in terms of neighboring nodes. In order to construct representations for a node in a graph, in addition to the features of the node and its immediate neighboring nodes, we also include more distant nodes in the calculations. In experimenting with a number of publicly available citation graph datasets, we show that this higher order neighbor visiting pays off by outperforming the original model especially when we have a limited number of available labeled data points for the training of the model.

Figures (2)

• Figure 1: Wall-clock training time per epoch for different order of neighborhood and different random graphs of $N$ nodes and $2N$ edges.
• Figure 2: Mean accuracy of each model per epoch when training on the Cora dataset. The curves show average and standard deviation of accuracy on each training epoch on validation and training data. We can see how the expanded models tend to learn faster from the data.