Graph Mixup on Approximate Gromov–Wasserstein Geodesics

Zhichen Zeng, Ruizhong Qiu, Zhe Xu, Zhining Liu, Yuchen Yan, Tianxin Wei, Lei Ying, Jingrui He, Hanghang Tong
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:58387-58406, 2024.

Abstract

Mixup, which generates synthetic training samples on the data manifold, has been shown to be highly effective in augmenting Euclidean data. However, finding a proper data manifold for graph data is non-trivial, as graphs are non-Euclidean data in disparate spaces. Though efforts have been made, most of the existing graph mixup methods neglect the intrinsic geodesic guarantee, thereby generating inconsistent sample-label pairs. To address this issue, we propose GeoMix to mixup graphs on the Gromov-Wasserstein (GW) geodesics. A joint space over input graphs is first defined based on the GW distance, and graphs are then transformed into the GW space through equivalence-preserving transformations. We further show that the linear interpolation of the transformed graph pairs defines a geodesic connecting the original pairs on the GW manifold, hence ensuring the consistency between generated samples and labels. An accelerated mixup algorithm on the approximate low-dimensional GW manifold is further proposed. Extensive experiments show that the proposed GeoMix promotes the generalization and robustness of GNN models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-zeng24e, title = {Graph Mixup on Approximate Gromov–{W}asserstein Geodesics}, author = {Zeng, Zhichen and Qiu, Ruizhong and Xu, Zhe and Liu, Zhining and Yan, Yuchen and Wei, Tianxin and Ying, Lei and He, Jingrui and Tong, Hanghang}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {58387--58406}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/zeng24e/zeng24e.pdf}, url = {https://proceedings.mlr.press/v235/zeng24e.html}, abstract = {Mixup, which generates synthetic training samples on the data manifold, has been shown to be highly effective in augmenting Euclidean data. However, finding a proper data manifold for graph data is non-trivial, as graphs are non-Euclidean data in disparate spaces. Though efforts have been made, most of the existing graph mixup methods neglect the intrinsic geodesic guarantee, thereby generating inconsistent sample-label pairs. To address this issue, we propose GeoMix to mixup graphs on the Gromov-Wasserstein (GW) geodesics. A joint space over input graphs is first defined based on the GW distance, and graphs are then transformed into the GW space through equivalence-preserving transformations. We further show that the linear interpolation of the transformed graph pairs defines a geodesic connecting the original pairs on the GW manifold, hence ensuring the consistency between generated samples and labels. An accelerated mixup algorithm on the approximate low-dimensional GW manifold is further proposed. Extensive experiments show that the proposed GeoMix promotes the generalization and robustness of GNN models.} }
Endnote
%0 Conference Paper %T Graph Mixup on Approximate Gromov–Wasserstein Geodesics %A Zhichen Zeng %A Ruizhong Qiu %A Zhe Xu %A Zhining Liu %A Yuchen Yan %A Tianxin Wei %A Lei Ying %A Jingrui He %A Hanghang Tong %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-zeng24e %I PMLR %P 58387--58406 %U https://proceedings.mlr.press/v235/zeng24e.html %V 235 %X Mixup, which generates synthetic training samples on the data manifold, has been shown to be highly effective in augmenting Euclidean data. However, finding a proper data manifold for graph data is non-trivial, as graphs are non-Euclidean data in disparate spaces. Though efforts have been made, most of the existing graph mixup methods neglect the intrinsic geodesic guarantee, thereby generating inconsistent sample-label pairs. To address this issue, we propose GeoMix to mixup graphs on the Gromov-Wasserstein (GW) geodesics. A joint space over input graphs is first defined based on the GW distance, and graphs are then transformed into the GW space through equivalence-preserving transformations. We further show that the linear interpolation of the transformed graph pairs defines a geodesic connecting the original pairs on the GW manifold, hence ensuring the consistency between generated samples and labels. An accelerated mixup algorithm on the approximate low-dimensional GW manifold is further proposed. Extensive experiments show that the proposed GeoMix promotes the generalization and robustness of GNN models.
APA
Zeng, Z., Qiu, R., Xu, Z., Liu, Z., Yan, Y., Wei, T., Ying, L., He, J. & Tong, H.. (2024). Graph Mixup on Approximate Gromov–Wasserstein Geodesics. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:58387-58406 Available from https://proceedings.mlr.press/v235/zeng24e.html.

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