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.

翻译：几何树以其树状布局和空间受限的节点与边为特征，这显著影响了其拓扑属性。这种固有的层次结构在神经元形态学和河流地貌学等领域起着至关重要的作用，但传统的图表示方法往往忽视了树结构的这些特定特征。为此，我们提出了一种专为几何树设计的新型表示学习框架。该框架首先采用了一种独特的消息传递神经网络，该网络在理论上可恢复几何结构，并具有旋转平移不变性。针对数据标签稀缺的问题，我们的方法还包含了两个创新的训练目标，这些目标反映了几何树的层次排序和几何结构。这使得无需显式标签即可实现完全自监督学习。我们在八个真实世界数据集上验证了该方法的有效性，证明了其表示几何树的能力。