Quaternion Graph Neural Networks
This work addresses the challenge of improving graph representation learning for researchers and practitioners in machine learning, though it appears incremental as it extends existing GNN methods to a different mathematical space.
The paper tackles the problem of learning graph representations by proposing Quaternion Graph Neural Networks (QGNN) to operate in Quaternion space instead of Euclidean space, achieving state-of-the-art results on benchmark datasets for graph classification, node classification, and knowledge graph completion.
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}.