Topologically Attributed Graphs for Shape Discrimination

Justin Curry, Washington Mio, Tom Needham, Osman Berat Okutan, Florian Russold
Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), PMLR 221:87-101, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v221-curry23a, title = {Topologically Attributed Graphs for Shape Discrimination}, author = {Curry, Justin and Mio, Washington and Needham, Tom and Okutan, Osman Berat and Russold, Florian}, booktitle = {Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML)}, pages = {87--101}, year = {2023}, editor = {Doster, Timothy and Emerson, Tegan and Kvinge, Henry and Miolane, Nina and Papillon, Mathilde and Rieck, Bastian and Sanborn, Sophia}, volume = {221}, series = {Proceedings of Machine Learning Research}, month = {28 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v221/curry23a/curry23a.pdf}, url = {https://proceedings.mlr.press/v221/curry23a.html}, 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.} }
Endnote
%0 Conference Paper %T Topologically Attributed Graphs for Shape Discrimination %A Justin Curry %A Washington Mio %A Tom Needham %A Osman Berat Okutan %A Florian Russold %B Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML) %C Proceedings of Machine Learning Research %D 2023 %E Timothy Doster %E Tegan Emerson %E Henry Kvinge %E Nina Miolane %E Mathilde Papillon %E Bastian Rieck %E Sophia Sanborn %F pmlr-v221-curry23a %I PMLR %P 87--101 %U https://proceedings.mlr.press/v221/curry23a.html %V 221 %X 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.
APA
Curry, J., Mio, W., Needham, T., Okutan, O.B. & Russold, F.. (2023). Topologically Attributed Graphs for Shape Discrimination. Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), in Proceedings of Machine Learning Research 221:87-101 Available from https://proceedings.mlr.press/v221/curry23a.html.

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