  Graphs are the most ubiquitous form of structured data representation used in
machine learning. They model, however, only pairwise relations between nodes
and are not designed for encoding the higher-order relations found in many
real-world datasets. To model such complex relations, hypergraphs have proven
to be a natural representation. Learning the node representations in a
hypergraph is more complex than in a graph as it involves information
propagation at two levels: within every hyperedge and across the hyperedges.
Most current approaches first transform a hypergraph structure to a graph for
use in existing geometric deep learning algorithms. This transformation leads
to information loss, and sub-optimal exploitation of the hypergraph's
expressive power. We present HyperSAGE, a novel hypergraph learning framework
that uses a two-level neural message passing strategy to accurately and
efficiently propagate information through hypergraphs. The flexible design of
HyperSAGE facilitates different ways of aggregating neighborhood information.
Unlike the majority of related work which is transductive, our approach,
inspired by the popular GraphSAGE method, is inductive. Thus, it can also be
used on previously unseen nodes, facilitating deployment in problems such as
evolving or partially observed hypergraphs. Through extensive experimentation,
we show that HyperSAGE outperforms state-of-the-art hypergraph learning methods
on representative benchmark datasets. We also demonstrate that the higher
expressive power of HyperSAGE makes it more stable in learning node
representations as compared to the alternatives.
