Hypergraph Joint Representation Learning for Hypervertices and Hyperedges via Cross Expansion

Hypergraph captures high-order information in structured data and obtains much attention in machine learning and data mining. Existing approaches mainly learn representations for hypervertices by transforming a hypergraph to a standard graph, or learn representations for hypervertices and hyperedges in separate spaces. In this paper, we propose a hypergraph expansion method to transform a hypergraph to a standard graph while preserving high-order information. Different from previous hypergraph expansion approaches like clique expansion and star expansion, we transform both hypervertices and hyperedges in the hypergraph to vertices in the expanded graph, and construct connections between hypervertices or hyperedges, so that richer relationships can be used in graph learning. Based on the expanded graph, we propose a learning model to embed hypervertices and hyperedges in a joint representation space. Compared with the method of learning separate spaces for hypervertices and hyperedges, our method is able to capture common knowledge involved in hypervertices and hyperedges, and also improve the data efficiency and computational efficiency. To better leverage structure information, we minimize the graph reconstruction loss to preserve the structure information in the model. We perform experiments on both hypervertex classification and hyperedge classification tasks to demonstrate the effectiveness of our proposed method.