Diss-l-ECT: Dissecting Graph Data with local Euler Characteristic Transforms

Julius von Rohrscheidt, Bastian Rieck

Keywords: topology, geometry, topological data analysis, graph learning, node classification, spatial alignment, interpretable graph learning

TL;DR: We present local Euler Characteristic Transforms and show its expressivity for interpretable node classification.

Abstract:

The Euler Characteristic Transform (ECT) is an efficiently-computable
geometrical-topological invariant that characterizes the global shape of data.
In this paper, we introduce the Local Euler Characteristic Transform (l-ECT), a novel extension of the ECT particularly designed to enhance expressivity and interpretability in graph representation learning.
Unlike traditional Graph Neural Networks (GNNs), which may lose critical local details through aggregation, the l-ECT provides a lossless representation of local neighborhoods.
This approach addresses key limitations in GNNs by preserving nuanced local structures while maintaining global interpretability.
Moreover, we construct a rotation-invariant metric based on l-ECTs for spatial alignment of data spaces.
Our method exhibits superior performance than standard GNNs on a variety of node classification tasks, particularly in graphs with high heterophily.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 3658