Quaternion Graph Neural Networks

TL;DR

This paper introduces Quaternion Graph Neural Networks (QGNN), which learn graph representations in hyper-complex quaternion space, leading to state-of-the-art results in graph and knowledge graph tasks.

Contribution

The paper proposes QGNN, a novel GNN model that operates in quaternion space, enhancing representation learning with hyper-complex algebra for improved performance.

Findings

QGNN achieves state-of-the-art results on graph classification datasets.

QGNN outperforms existing models on knowledge graph completion benchmarks.

Quaternion space provides meaningful computations for graph learning.

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}.