This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to retrieve and distinguish variations in the connectivity structure of the data but also geometric differences of the network branches. Our proposed approach relies on the extraction of a specifically curated and explicit set of topological, geometric and directional features, designed to satisfy key invariance properties. We leverage the resulting feature representation for tasks such as group comparison, clustering and classification on cohorts of shape graphs. The effectiveness of this representation is evaluated on several real-world datasets including urban road/street networks, neuronal traces and astrocyte imaging. These results are benchmarked against several alternative methods, both feature-based and not.

翻译：本文提出并展示了一种用于形状图数据集统计分析的计算流程，即嵌入二维或三维空间的几何网络。与传统抽象图不同，我们的目标不仅是检索和区分数据连接结构的变化，还包括网络分支的几何差异。我们提出的方法依赖于提取一组经过专门筛选的、显式的拓扑、几何和方向特征，这些特征设计用于满足关键的不变性特性。我们利用所得特征表示进行形状图群组的比较、聚类和分类等任务。该表示的有效性在多个实际数据集上进行了评估，包括城市道路/街道网络、神经元追踪和星形胶质细胞成像。这些结果与多种替代方法（包括基于特征和非基于特征的方法）进行了基准测试。