Explainable Hyperlink Prediction: A Hypergraph Edit Distance-Based Approach

Link prediction is a significant technique to generate latent interactions for the applications of recommendation in large graphs. As the interactions to be predicted often occur among more than two objects, we pay attention to solving the novel problem of predicting the interactions in hypergraphs. Previous studies focus mainly on predicting binary relations; most of those techniques cannot be directly applied to predict multiple relations. In this work, we study the problem of edge prediction in hypergraphs, where we use a concept, Hypergraph Edit Distance (abbreviated as HGED), to measure the similarity of two nodes. Based on HGED, we can record a Hypergraph Edit Path while searching the optimal edit distance, thus this path enables to explain why one node is similar to another node since their neighborhood structure can be edited to be isomorphic following the edit path. We first propose a general framework which can compute the edit distance of neighborhood structure for two nodes in hypergraph. To improve the efficiency, we propose a BFS search-based method with several tightening lower bounds and upper bounds estimation. To predict the multiple relations, we introduce a cluster model in which nodes in each hyperedge are restricted by the hypergraph edit distance. We further present an on-demand algorithm for computing HGED, which substantially avoids redundant computations. Finally, we conduct extensive empirical studies on real hypergraph datasets, and the results demonstrate the effectiveness, efficiency and scalability of our algorithms.