Quaternion Graph Neural Networks

Dai Quoc Nguyen, Tu Dinh Nguyen, Dinh Phung
Proceedings of The 13th Asian Conference on Machine Learning, PMLR 157:236-251, 2021.

Abstract

Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space. Beyond the Euclidean space, learning representation and embeddings in hyper-complex space have also shown to be a promising and effective approach. To this end, we propose Quaternion Graph Neural Networks (QGNN) to learn graph representations within the Quaternion space. As demonstrated, the Quaternion space, a hyper-complex vector space, provides highly meaningful computations and analogical calculus through Hamilton product compared to the Euclidean and complex vector spaces. Our QGNN obtains state-of-the-art results on a range of benchmark datasets for graph classification and node classification. Besides, regarding knowledge graphs, our QGNN-based embedding model achieves state-of-the-art results on three new and challenging benchmark datasets for knowledge graph completion. Our code is available at: \url{https://github.com/daiquocnguyen/QGNN}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v157-nguyen21a, title = {Quaternion Graph Neural Networks}, author = {Nguyen, Dai Quoc and Nguyen, Tu Dinh and Phung, Dinh}, booktitle = {Proceedings of The 13th Asian Conference on Machine Learning}, pages = {236--251}, year = {2021}, editor = {Balasubramanian, Vineeth N. and Tsang, Ivor}, volume = {157}, series = {Proceedings of Machine Learning Research}, month = {17--19 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v157/nguyen21a/nguyen21a.pdf}, url = {https://proceedings.mlr.press/v157/nguyen21a.html}, abstract = {Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space. Beyond the Euclidean space, learning representation and embeddings in hyper-complex space have also shown to be a promising and effective approach. To this end, we propose Quaternion Graph Neural Networks (QGNN) to learn graph representations within the Quaternion space. As demonstrated, the Quaternion space, a hyper-complex vector space, provides highly meaningful computations and analogical calculus through Hamilton product compared to the Euclidean and complex vector spaces. Our QGNN obtains state-of-the-art results on a range of benchmark datasets for graph classification and node classification. Besides, regarding knowledge graphs, our QGNN-based embedding model achieves state-of-the-art results on three new and challenging benchmark datasets for knowledge graph completion. Our code is available at: \url{https://github.com/daiquocnguyen/QGNN}.} }
Endnote
%0 Conference Paper %T Quaternion Graph Neural Networks %A Dai Quoc Nguyen %A Tu Dinh Nguyen %A Dinh Phung %B Proceedings of The 13th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Vineeth N. Balasubramanian %E Ivor Tsang %F pmlr-v157-nguyen21a %I PMLR %P 236--251 %U https://proceedings.mlr.press/v157/nguyen21a.html %V 157 %X Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space. Beyond the Euclidean space, learning representation and embeddings in hyper-complex space have also shown to be a promising and effective approach. To this end, we propose Quaternion Graph Neural Networks (QGNN) to learn graph representations within the Quaternion space. As demonstrated, the Quaternion space, a hyper-complex vector space, provides highly meaningful computations and analogical calculus through Hamilton product compared to the Euclidean and complex vector spaces. Our QGNN obtains state-of-the-art results on a range of benchmark datasets for graph classification and node classification. Besides, regarding knowledge graphs, our QGNN-based embedding model achieves state-of-the-art results on three new and challenging benchmark datasets for knowledge graph completion. Our code is available at: \url{https://github.com/daiquocnguyen/QGNN}.
APA
Nguyen, D.Q., Nguyen, T.D. & Phung, D.. (2021). Quaternion Graph Neural Networks. Proceedings of The 13th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 157:236-251 Available from https://proceedings.mlr.press/v157/nguyen21a.html.

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