  Link prediction typically studies the probability of future interconnection
among nodes with the observation in a single social network. More often than
not, real scenario is presented as a multiplex network with common (anchor)
users active in multiple social networks. In the literature, most existing
works study either the intra-link prediction in a single network or inter-link
prediction among networks (a.k.a. network alignment), and consider two learning
tasks are independent from each other, which is still away from the fact. On
the representation space, the vast majority of existing methods are built upon
the traditional Euclidean space, unaware of the inherent geometry of social
networks. The third issue is on the scarce anchor users. Annotating anchor
users is laborious and expensive, and thus it is impractical to work with
quantities of anchor users. Herein, in light of the issues above, we propose to
study a challenging yet practical problem of Geometry-aware Collective Link
Prediction across Multiplex Network. To address this problem, we present a
novel contrastive model, RCoCo, which collaborates intra- and inter-network
behaviors in Riemannian spaces. In RCoCo, we design a curvature-aware graph
attention network ($\kappa-$GAT), conducting attention mechanism in Riemannian
manifold whose curvature is estimated by the Ricci curvatures over the network.
Thereafter, we formulate intra- and inter-contrastive loss in the manifolds, in
which we augment graphs by exploring the high-order structure of community and
information transfer on anchor users. Finally, we conduct extensive experiments
with 14 strong baselines on 8 real-world datasets, and show the effectiveness
of RCoCo.
