Mustafa Coşkun

Mustafa Coşkun, Ananth Grama, Mehmet Koyutürk

Spectral Graph Convolutional Networks (GCNs) have gained popularity in graph machine learning applications due, in part, to their flexibility in specification of network propagation rules. These propagation rules are often constructed as polynomial filters whose coefficients are learned using label information during training. In contrast to learned polynomial filters, explicit filter functions are useful in capturing relationships between network topology and distribution of labels across the network. A number of algorithms incorporating either approach have been proposed; however the relationship between filter functions and polynomial approximations is not fully resolved. This is largely due to the ill-conditioned nature of the linear systems that must be solved to derive polynomial approximations of filter functions. To address this challenge, we propose a novel Arnoldi orthonormalization-based algorithm, along with a unifying approach, called G-Arnoldi-GCN that can efficiently and effectively approximate a given filter function with a polynomial. We evaluate G-Arnoldi-GCN in the context of multi-class node classification across ten datasets with diverse topological characteristics. Our experiments show that G-Arnoldi-GCN consistently outperforms state-of-the-art methods when suitable filter functions are employed. Overall, G-Arnoldi-GCN opens important new directions in graph machine learning by enabling the explicit design and application of diverse filter functions. Code link: https://github.com/mustafaCoskunAgu/GArnoldi-GCN

Mustafa Coskun, Burcu Bakir Gungor, Mehmet Koyuturk

In recent years, Graph Convolutional Networks (GCNs) and their variants have been widely utilized in learning tasks that involve graphs. These tasks include recommendation systems, node classification, among many others. In node classification problem, the input is a graph in which the edges represent the association between pairs of nodes, multi-dimensional feature vectors are associated with the nodes, and some of the nodes in the graph have known labels. The objective is to predict the labels of the nodes that are not labeled, using the nodes features, in conjunction with graph topology. While GCNs have been successfully applied to this problem, the caveats that they inherit from traditional deep learning models pose significant challenges to broad utilization of GCNs in node classification. One such caveat is that training a GCN requires a large number of labeled training instances, which is often not the case in realistic settings. To remedy this requirement, state-of-the-art methods leverage network diffusion-based approaches to propagate labels across the network before training GCNs. However, these approaches ignore the tendency of the network diffusion methods in biasing proximity with centrality, resulting in the propagation of labels to the nodes that are well-connected in the graph. To address this problem, here we present an alternate approach to extrapolating node labels in GCNs in the following three steps: (i) clustering of the network to identify communities, (ii) use of network diffusion algorithms to quantify the proximity of each node to the communities, thereby obtaining a low-dimensional topological profile for each node, (iii) comparing these topological profiles to identify nodes that are most similar to the labeled nodes.

Mustafa Coskun

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}.