  Link prediction infers potential links from observed networks, and is one of
the essential problems in network analyses. In contrast to traditional graph
representation modeling which only predicts two-way pairwise relations, we
propose a novel tensor-based joint network embedding approach on simultaneously
encoding pairwise links and hyperlinks onto a latent space, which captures the
dependency between pairwise and multi-way links in inferring potential
unobserved hyperlinks. The major advantage of the proposed embedding procedure
is that it incorporates both the pairwise relationships and subgroup-wise
structure among nodes to capture richer network information. In addition, the
proposed method introduces a hierarchical dependency among links to infer
potential hyperlinks, and leads to better link prediction. In theory we
establish the estimation consistency for the proposed embedding approach, and
provide a faster convergence rate compared to link prediction utilizing
pairwise links or hyperlinks only. Numerical studies on both simulation
settings and Facebook ego-networks indicate that the proposed method improves
both hyperlink and pairwise link prediction accuracy compared to existing link
prediction algorithms.
