  Network embedding has recently attracted lots of attentions in data mining.
Existing network embedding methods mainly focus on networks with pairwise
relationships. In real world, however, the relationships among data points
could go beyond pairwise, i.e., three or more objects are involved in each
relationship represented by a hyperedge, thus forming hyper-networks. These
hyper-networks pose great challenges to existing network embedding methods when
the hyperedges are indecomposable, that is to say, any subset of nodes in a
hyperedge cannot form another hyperedge. These indecomposable hyperedges are
especially common in heterogeneous networks. In this paper, we propose a novel
Deep Hyper-Network Embedding (DHNE) model to embed hyper-networks with
indecomposable hyperedges. More specifically, we theoretically prove that any
linear similarity metric in embedding space commonly used in existing methods
cannot maintain the indecomposibility property in hyper-networks, and thus
propose a new deep model to realize a non-linear tuplewise similarity function
while preserving both local and global proximities in the formed embedding
space. We conduct extensive experiments on four different types of
hyper-networks, including a GPS network, an online social network, a drug
network and a semantic network. The empirical results demonstrate that our
method can significantly and consistently outperform the state-of-the-art
algorithms.
