Representation Learning of Geometric Trees

TL;DR

This paper introduces a novel self-supervised representation learning framework for geometric trees, leveraging a specialized message passing neural network that captures hierarchical and geometric features while being rotation-translation invariant.

Contribution

It presents a new geometric tree-specific neural network and training targets enabling effective self-supervised learning without explicit labels.

Findings

Effective on eight real-world datasets

Captures hierarchical and geometric structures

Rotation-translation invariant representations

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.