  Graph Convolution Network (GCN) has been widely applied in recommender
systems for its representation learning capability on user and item embeddings.
However, GCN is vulnerable to noisy and incomplete graphs, which are common in
real world, due to its recursive message propagation mechanism. In the
literature, some work propose to remove the feature transformation during
message propagation, but making it unable to effectively capture the graph
structural features. Moreover, they model users and items in the Euclidean
space, which has been demonstrated to have high distortion when modeling
complex graphs, further degrading the capability to capture the graph
structural features and leading to sub-optimal performance. To this end, in
this paper, we propose a simple yet effective Quaternion-based Graph
Convolution Network (QGCN) recommendation model. In the proposed model, we
utilize the hyper-complex Quaternion space to learn user and item
representations and feature transformation to improve both performance and
robustness. Specifically, we first embed all users and items into the
Quaternion space. Then, we introduce the quaternion embedding propagation
layers with quaternion feature transformation to perform message propagation.
Finally, we combine the embeddings generated at each layer with the mean
pooling strategy to obtain the final embeddings for recommendation. Extensive
experiments on three public benchmark datasets demonstrate that our proposed
QGCN model outperforms baseline methods by a large margin.
