  Graph representation learning received increasing attentions in recent years.
Most of existing methods ignore the complexity of the graph structures and
restrict graphs in a single constant-curvature representation space, which is
only suitable to particular kinds of graph structure indeed. Additionally,
these methods follow the supervised or semi-supervised learning paradigm, and
thereby notably limit their deployment on the unlabeled graphs in real
applications. To address these aforementioned limitations, we take the first
attempt to study the self-supervised graph representation learning in the
mixed-curvature spaces. In this paper, we present a novel Self-supervised
Mixed-curvature Graph Neural Network (SelfMGNN). Instead of working on one
single constant-curvature space, we construct a mixed-curvature space via the
Cartesian product of multiple Riemannian component spaces and design
hierarchical attention mechanisms for learning and fusing the representations
across these component spaces. To enable the self-supervisd learning, we
propose a novel dual contrastive approach. The mixed-curvature Riemannian space
actually provides multiple Riemannian views for the contrastive learning. We
introduce a Riemannian projector to reveal these views, and utilize a
well-designed Riemannian discriminator for the single-view and cross-view
contrastive learning within and across the Riemannian views. Finally, extensive
experiments show that SelfMGNN captures the complicated graph structures in
reality and outperforms state-of-the-art baselines.
