Exploring the efficacy of a graph classification GNN in learning non-linear graph metrics

Graph-structured data is common in many felds, including social networks, biological networks, and recommendation systems. The complexity of relationships in such data frequently necessitates the use of advanced modeling approaches to derive relevant insights. With the increasingly large network datasets being made available, deep learning is becoming a more relevant methodology for their exploration. Deep learning architectures which have graph inputs are called Graph Neural Networks (GNNs). One area in particular where great efforts have been made to gather population-wide data is in brain connectomics. The UK BioBank, for example has plans for up to 100,000 MRI scans which can be used for processing into brain connectomes. An important example of a graph classifcation GNN model for use on such data is the Brain Network Convolutional Neural Network (BrainNetCNN) model [1]. The BrainNetCNN is a CNN with special “cross-shaped” kernels for dealing with graph adjacency matrices. However, recent studies have repeatedly shown that the BrainNetCNN (among other GNNs) fails to outperform simpler, linear predictive models such as linear ridge regression in predicting population characteristics and clinical variables [2] [3] [4] [5].

This could be because most of the important characteristic/diagnostic information retrievable from brain networks is linear in nature, or there is still not enough data available to train GNNs on brain networks. But it could also be that developing more powerful models which can better identify more interesting relationships in the data with greater effciency will signifcantly improve predictive power. In order to begin analysing this, here we study how well the BrainNetCNN can learn non-linear patterns and structural characteristics– clustering coeffcient, routing effciency, degree variance, diffusion effciency, and assortativity– in three different types of synthetic graph datasets: Erdos-Renyi graphs, Barabasi-Albert graphs, and random geometric graphs. We use linear ridge regression as a baseline for comparison against linear modelling. We provide this baseline frstly to verify that BrainNetCNN can actually outperform linear models on non-linear metric learning, and secondly to enhance insights into model performance across the different graph metrics and graph datasets studied.