Extended Graph Assessment Metrics for Regression and Weighted Graphs

When re-structuring patient cohorts into so-called population graphs, initially independent patients can be incorporated into one interconnected graph structure. This population graph can then be used for medical downstream tasks using graph neural networks (GNNs). The construction of a suitable graph structure is a challenging step in the learning pipeline that can have a severe impact on model performance. To this end, different graph assessment metrics have been introduced to evaluate graph structures. However, these metrics are limited to classification tasks and discrete adjacency matrices, only covering a small subset of real-world applications. In this work, we introduce extended graph assessment metrics (GAMs) for regression tasks and weighted graphs. We focus on two GAMs in particular: homophily and cross-class neighbourhood similarity (CCNS). We extend the notion of GAMs to more than one hop, define homophily for regression tasks, as well as continuous adjacency matrices, and propose a lightweight CCNS distance for discrete and continuous adjacency matrices. We show the correlation of these metrics with model performance on different medical population graphs and under different learning settings, using the TADPOLE and UKBB datasets \(^{1}\) (The source code can be found at https://github.com/tamaramueller/ExtendedGAMs ).