RCoCo: Contrastive Collective Link Prediction across Multiplex Network in Riemannian Space

TL;DR

This work designs a novel contrastive model, RCoCo, which collaborates intra- and inter-network behaviors in Riemannian spaces, and designs a curvature-aware graph attention network in Riemannian manifold whose curvature is estimated by the Ricci curvatures over the network.

Abstract

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 ($κ-$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.

Figures (6)

• Figure 1: Overall architecture of RCoCo. For two networks with anchor users (the dotted line in the figure represents the anchor user), we first designed a curvature estimator to adapt the geometry of each graph which employs the Ricci curvature. Then with the curvature estimated $\kappa_{i}$, $\kappa$-GAT conducts intra- and inter- network attention aggregation in the manifold, where $e^{in}(x^{s},x^{s})$ in figure represents intra network attention, and $e^{er}(x^{s},x^{t})$ represents intra network attention. Finally, we conduct intra- and inter-contrastive learning in the manifold via three loss functions.
• Figure 2: Node-Supernode contrastive Learning. We first group the community members as a supernode with I-Louvain algorithm, and then contrast the original node view and generated supernode view.
• Figure 3: Efficiency of baselines and RCoCo. Taking the running time of RCoCo as the unit time, $(a)$ is the efficiency of link-prediction baselines relative to RCoCo, $(b)$ is the efficiency of user alignment baselines relative to RCoCo.
• Figure 4: Alignment results on DBpedia$_{\text{CH}}$-DBpedia$_{\text{EN}}$ and AMiner-DBLP datasets in terms of $MRR@10$.
• Figure 5: Results of RCoCo performs intra-link prediction on Twitter$_A$ and DBLP datasets in different dimensions $\{8, 16, 32, 64, 128\}$ (in terms of AUC).