When re-structuring patient cohorts into so-called population graphs, initially independent data points 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 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 continuous adjacency matrices. We focus on two GAMs in specific: \textit{homophily} and \textit{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 light-weight 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.

翻译：在将患者队列重构成所谓的群体图时，原本独立的数据点可被整合到一个相互连接的图结构中。该群体图可进一步用于图神经网络（GNN）的医学下游任务。构建合适的图结构是学习流程中具有挑战性的环节，会对模型性能产生重大影响。为此，研究人员引入了多种图评估指标来评估图结构。然而，现有指标仅适用于分类任务和离散邻接矩阵，仅覆盖了真实世界应用中的一小部分场景。本研究针对回归任务和连续邻接矩阵，引入了扩展图评估指标（GAMs）。我们重点聚焦两种具体GAM指标：同质性（homophily）和跨类邻域相似性（CCNS）。我们将GAM概念扩展到多跳场景，定义了面向回归任务及连续邻接矩阵的同质性指标，并针对离散与连续邻接矩阵提出了一种轻量级CCNS距离度量。通过在不同医学群体图及不同学习设置下的实验，我们展示了这些指标与模型性能之间的相关性。