Intrinsic graph topological correlation for graph convolutional network propagation

Abstract

Recently, Graph Convolutional Networks (GCNs) and their variants become popular to learn graph-related tasks. These tasks include link prediction, node classification, and node embedding, among many others. In the node classification problem, the input is a graph with some labeled nodes and the features associated with these nodes and the objective is to predict the unlabeled nodes. While the GCNs have been successfully applied to this problem, some caveats that are inherited from classical deep learning remain unsolved. One such inherited caveat is that, during classification, GCNs only consider the nodes that are a few neighbors away from the labeled nodes. However, considering only a few steps away nodes could not effectively exploit the underlying graph topological information. To remedy this problem, the state-of-the-art methods leverage the network diffusion approaches, such as personalized PageRank and its variants, to fully account for the graph topology. However, these approaches overlook the fact that the network diffusion methods favour high degree nodes in the graph, resulting in the propagation of the labels to the unlabeled,hub nodes. In order to overcome bias, in this paper, we propose to utilize a dimensionality reduction technique, which is conjugate with personalized PageRank. Testing on four real-world networks that are commonly used in benchmarking GCNs' performance for the node classification task, we systematically evaluate the performance of the proposed methodology and show that our approach outperforms existing methods for wide ranges of parameter values. Since our method requires only a few training epochs, it releases the heavy training burden of GCNs. The source code of the proposed method is freely available at https://github.com/mustafaCoskunAgu/ScNP/blob/master/TRJMain.m.