Dynamic hypergraph embedding onto concentric hypersphere manifold intended for effective visualization

Abstract Hypergraph is a graph structure that can efficiently express the relationship of multiple nodes and has attracted attention in recent years. As with normal graphs, the structure changes every moment, and it is an important research topic in graph mining to capture structural changes. Many existing graph embedding methods focus on prediction tasks, and few focus on the visualization of structural changes. In this study, we aim to output embeddings for effective visualization in terms of spatial efficiency, node classification accuracy, graph structure maintenance, computational efficiency, and structural change detection performance. Our proposed method gets inspired by modularity maximization, quantifies connection strength between hypernodes and hyperedges, and embeds hypernodes on the surface of concentric spheres with a radius equal to the timestep, where a spherical surface has a wide area in the middle range. These devices are expected to correspond to the following two characteristics: (1) a graph has more node pairs whose distances are middle-range than short- and long-range; (2) a growing graph generally has an increasing number of nodes. Evaluation experiments using multiple real hypergraphs show that the proposed method is superior to existing visualization methods in the abovementioned terms.