  Network representation learning has aroused widespread interests in recent
years. While most of the existing methods deal with edges as pairwise
relationships, only a few studies have been proposed for hyper-networks to
capture more complicated tuplewise relationships among multiple nodes. A
hyper-network is a network where each edge, called hyperedge, connects an
arbitrary number of nodes. Different from conventional networks, hyper-networks
have certain degrees of indecomposability such that the nodes in a subset of a
hyperedge may not possess a strong relationship. That is the main reason why
traditional algorithms fail in learning representations in hyper-networks by
simply decomposing hyperedges into pairwise relationships. In this paper, we
firstly define a metric to depict the degrees of indecomposability for
hyper-networks. Then we propose a new concept called hyper-path and design
hyper-path-based random walks to preserve the structural information of
hyper-networks according to the analysis of the indecomposability. Then a
carefully designed algorithm, Hyper-gram, utilizes these random walks to
capture both pairwise relationships and tuplewise relationships in the whole
hyper-networks. Finally, we conduct extensive experiments on several real-world
datasets covering the tasks of link prediction and hyper-network
reconstruction, and results demonstrate the rationality, validity, and
effectiveness of our methods compared with those existing state-of-the-art
models designed for conventional networks or hyper-networks.
