  Graph representation learning for hypergraphs can be used to extract patterns
among higher-order interactions that are critically important in many real
world problems. Current approaches designed for hypergraphs, however, are
unable to handle different types of hypergraphs and are typically not generic
for various learning tasks. Indeed, models that can predict variable-sized
heterogeneous hyperedges have not been available. Here we develop a new
self-attention based graph neural network called Hyper-SAGNN applicable to
homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We
perform extensive evaluations on multiple datasets, including four benchmark
network datasets and two single-cell Hi-C datasets in genomics. We demonstrate
that Hyper-SAGNN significantly outperforms the state-of-the-art methods on
traditional tasks while also achieving great performance on a new task called
outsider identification. Hyper-SAGNN will be useful for graph representation
learning to uncover complex higher-order interactions in different
applications.
