Topologically Attributed Graphs for Shape Discrimination

Published: 18 Jun 2023, Last Modified: 30 Jun 2023TAGML2023 OralEveryoneRevisions
Keywords: Topological Data Analysis, Reeb Graph, Mapper, Persistent Homology, Shape Classification
Abstract: 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 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.
Supplementary Materials: pdf
Type Of Submission: Proceedings Track (8 pages)
Submission Number: 44