Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such as neuron morphology and river geomorphology, but traditional graph representation methods often overlook these specific characteristics of tree structures. To address this, we introduce a new representation learning framework tailored for geometric trees. It first features a unique message passing neural network, which is both provably geometrical structure-recoverable and rotation-translation invariant. To address the data label scarcity issue, our approach also includes two innovative training targets that reflect the hierarchical ordering and geometric structure of these geometric trees. This enables fully self-supervised learning without explicit labels. We validate our method's effectiveness on eight real-world datasets, demonstrating its capability to represent geometric trees.

本研究解决了传统图表示方法未能充分利用几何树的层次结构和空间约束特征的问题。提出了一种新的表示学习框架，采用消息传递神经网络，并引入创新的自监督学习目标，能够有效表征几何树。通过在八个真实数据集上的验证，显示了该方法在几何树表示上的出色能力。

几何树的表示学习