  Hypergraph visualization has many applications in network data analysis.
Recently, a polygon-based representation for hypergraphs has been proposed with
demonstrated benefits. However, the polygon-based layout often suffers from
excessive self-intersections when the input dataset is relatively large. In
this paper, we propose a framework in which the hypergraph is iteratively
simplified through a set of atomic operations. Then, the layout of the simplest
hypergraph is optimized and used as the foundation for a reverse process that
brings the simplest hypergraph back to the original one, but with an improved
layout. At the core of our approach is the set of atomic simplification
operations and an operation priority measure to guide the simplification
process. In addition, we introduce necessary definitions and conditions for
hypergraph planarity within the polygon representation. We extend our approach
to handle simultaneous simplification and layout optimization for both the
hypergraph and its dual. We demonstrate the utility of our approach with
datasets from a number of real-world applications.
