Representation Learning of Geometric Trees

• URL: http://arxiv.org/abs/2408.08799v1
• Date: Fri, 16 Aug 2024 15:16:35 GMT
• Title: Representation Learning of Geometric Trees
• Authors: Zheng Zhang, Allen Zhang, Ruth Nelson, Giorgio Ascoli, Liang Zhao,
• Abstract summary: 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. We validate our method's effectiveness on eight real-world datasets, demonstrating its capability to represent geometric trees.
• Score: 9.280083998326285
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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