# Topologically Attributed Graphs for Shape Discrimination

arXiv: https://arxiv.org/abs/2306.17805 · HTML: https://mlsanity.com/paper/2306.17805/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2023.

## Built on by (most cited first, 2 of 2)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Structured Learning on Mapper Representations](https://mlsanity.com/paper/2608.22044/) (2026)

## Abstract (arXiv)

In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.