Motif-Aware Riemannian Graph Neural Network with Generative-Contrastive Learning
Li Sun, Zhenhao Huang, Zixi Wang, Feiyang Wang, Hao Peng, Philip S. Yu
Abstract
Graphs are typical non-Euclidean data of complex structures. In recent years, Riemannian graph representation learning has emerged as an exciting alternative to Euclidean ones. However, Riemannian methods are still in an early stage: most of them present a single curvature (radius) regardless of structural complexity, suffer from numerical instability due to the exponential/logarithmic map, and lack the ability to capture motif regularity. In light of the issues above, we propose the problem of Motif-aware Riemannian Graph Representation Learning, seeking a numerically stable encoder to capture motif regularity in a diverse-curvature manifold without labels. To this end, we present a novel Motif-aware Riemannian model with Generative-Contrastive learning (MotifRGC), which conducts a minmax game in Riemannian manifold in a self-supervised manner. First, we propose a new type of Riemannian GCN (D-GCN), in which we construct a diverse-curvature manifold by a product layer with the diversified factor, and replace the exponential/logarithmic map by a stable kernel layer. Second, we introduce a motif-aware Riemannian generative-contrastive learning to capture motif regularity in the constructed manifold and learn motif-aware node representation without external labels. Empirical results show the superiority of MofitRGC.
BibTeX
@article{Sun_Huang_Wang_Wang_Peng_Yu_2024, title={Motif-Aware Riemannian Graph Neural Network with Generative-Contrastive Learning}, volume={38}, url={https://ojs.aaai.org/index.php/AAAI/article/view/28754}, DOI={10.1609/aaai.v38i8.28754}, abstractNote={Graphs are typical non-Euclidean data of complex structures. In recent years, Riemannian graph representation learning has emerged as an exciting alternative to Euclidean ones. However, Riemannian methods are still in an early stage: most of them present a single curvature (radius) regardless of structural complexity, suffer from numerical instability due to the exponential/logarithmic map, and lack the ability to capture motif regularity. In light of the issues above, we propose the problem of Motif-aware Riemannian Graph Representation Learning, seeking a numerically stable encoder to capture motif regularity in a diverse-curvature manifold without labels. To this end, we present a novel Motif-aware Riemannian model with Generative-Contrastive learning (MotifRGC), which conducts a minmax game in Riemannian manifold in a self-supervised manner. First, we propose a new type of Riemannian GCN (D-GCN), in which we construct a diverse-curvature manifold by a product layer with the diversified factor, and replace the exponential/logarithmic map by a stable kernel layer. Second, we introduce a motif-aware Riemannian generative-contrastive learning to capture motif regularity in the constructed manifold and learn motif-aware node representation without external labels. Empirical results show the superiority of MofitRGC.}, number={8}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Sun, Li and Huang, Zhenhao and Wang, Zixi and Wang, Feiyang and Peng, Hao and Yu, Philip S.}, year={2024}, month={Mar.}, pages={9044-9052} }