Graph Convolutional Networks Meet with High Dimensionality Reduction

Recently, Graph Convolutional Networks (GCNs) and their variants have been receiving many research interests for learning graph-related tasks. While the GCNs have been successfully applied to this problem, some caveats inherited from classical deep learning still remain as open research topics in the context of the node classification problem. One such inherited caveat is that GCNs only consider the nodes that are a few propagations away from the labeled nodes to classify them. However, taking only a few propagation steps away nodes into account defeats the purpose of using the graph topological information in the GCNs. To remedy this problem, the-state-of-the-art methods leverage the network diffusion approaches, namely personalized page rank and its variants, to fully account for the graph topology, {\em after} they use the Neural Networks in the GCNs. However, these approaches overlook the fact that the network diffusion methods favour high degree nodes in the graph, resulting in the propagation of labels to unlabeled centralized, hub, nodes. To address this biasing hub nodes problem, in this paper, we propose to utilize a dimensionality reduction technique conjugate with personalized page rank so that we can both take advantage from graph topology and resolve the hub node favouring problem for GCNs. Here, our approach opens a new holistic road for message passing phase of GCNs by suggesting the usage of other proximity matrices instead of well-known Laplacian. Testing on two real-world networks that are commonly used in benchmarking GCNs' performance for the node classification context, we systematically evaluate the performance of the proposed methodology and show that our approach outperforms existing methods for wide ranges of parameter values with very limited deep learning training {\em epochs}.