Efficient Representation Learning for Higher-Order Data With Simplicial Complexes

Ruochen Yang, Frederic Sala, Paul Bogdan
Proceedings of the First Learning on Graphs Conference, PMLR 198:13:1-13:21, 2022.

Abstract

Graph-based machine learning is experiencing explosive growth, driven by impressive recent developments and wide applicability. Typical approaches for graph representation learning predominantly focus on pairwise interactions, while neglecting the patterns of higher-order interactions common to complex systems. This paper explores many-body interaction models, centering on simplicial complexes. From a theoretical point of view, we offer a pair of insights illustrating why higher-order models are necessary, why non-graph-based models generally cannot generalize well, while graph-based models may be able to do so. We conduct experiments on synthetic data, co-citation networks, co-authorship networks and gene-disease associations and show that simplicial complexes with certain relaxations can more efficiently capture underlying higher-order structures than non-graph structure, regular graph, hypergraph, and traditional simplicial complex-based learning frameworks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v198-yang22a, title = {Efficient Representation Learning for Higher-Order Data With Simplicial Complexes}, author = {Yang, Ruochen and Sala, Frederic and Bogdan, Paul}, booktitle = {Proceedings of the First Learning on Graphs Conference}, pages = {13:1--13:21}, year = {2022}, editor = {Rieck, Bastian and Pascanu, Razvan}, volume = {198}, series = {Proceedings of Machine Learning Research}, month = {09--12 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v198/yang22a/yang22a.pdf}, url = {https://proceedings.mlr.press/v198/yang22a.html}, abstract = {Graph-based machine learning is experiencing explosive growth, driven by impressive recent developments and wide applicability. Typical approaches for graph representation learning predominantly focus on pairwise interactions, while neglecting the patterns of higher-order interactions common to complex systems. This paper explores many-body interaction models, centering on simplicial complexes. From a theoretical point of view, we offer a pair of insights illustrating why higher-order models are necessary, why non-graph-based models generally cannot generalize well, while graph-based models may be able to do so. We conduct experiments on synthetic data, co-citation networks, co-authorship networks and gene-disease associations and show that simplicial complexes with certain relaxations can more efficiently capture underlying higher-order structures than non-graph structure, regular graph, hypergraph, and traditional simplicial complex-based learning frameworks.} }
Endnote
%0 Conference Paper %T Efficient Representation Learning for Higher-Order Data With Simplicial Complexes %A Ruochen Yang %A Frederic Sala %A Paul Bogdan %B Proceedings of the First Learning on Graphs Conference %C Proceedings of Machine Learning Research %D 2022 %E Bastian Rieck %E Razvan Pascanu %F pmlr-v198-yang22a %I PMLR %P 13:1--13:21 %U https://proceedings.mlr.press/v198/yang22a.html %V 198 %X Graph-based machine learning is experiencing explosive growth, driven by impressive recent developments and wide applicability. Typical approaches for graph representation learning predominantly focus on pairwise interactions, while neglecting the patterns of higher-order interactions common to complex systems. This paper explores many-body interaction models, centering on simplicial complexes. From a theoretical point of view, we offer a pair of insights illustrating why higher-order models are necessary, why non-graph-based models generally cannot generalize well, while graph-based models may be able to do so. We conduct experiments on synthetic data, co-citation networks, co-authorship networks and gene-disease associations and show that simplicial complexes with certain relaxations can more efficiently capture underlying higher-order structures than non-graph structure, regular graph, hypergraph, and traditional simplicial complex-based learning frameworks.
APA
Yang, R., Sala, F. & Bogdan, P.. (2022). Efficient Representation Learning for Higher-Order Data With Simplicial Complexes. Proceedings of the First Learning on Graphs Conference, in Proceedings of Machine Learning Research 198:13:1-13:21 Available from https://proceedings.mlr.press/v198/yang22a.html.

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