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.

翻译：超图可视化在网络数据分析中具有诸多应用。近期，一种基于多边形的超图表示方法被提出并展现出显著优势。然而，当输入数据集规模较大时，这种多边形布局常因过度自交而产生问题。本文提出一种框架，通过一系列原子操作迭代简化超图，随后优化最简超图的布局，并将其作为逆过程的基础，使最简超图恢复至原始状态，同时获得优化后的布局。该方法的核心是一组原子简化操作及用于指导简化过程的操作优先级度量。此外，我们在多边形表示框架内引入超图平面性的必要定义与条件。我们将该方法扩展至超图及其对偶图的同步简化与布局优化。通过多个实际应用数据集验证了该方法的有效性。