Modeling multi-way relations with hypergraph embedding

Hypergraph is a data structure commonly used to represent connections and relations between multiple objects. Embedding a hypergraph into a low-dimensional space and representing each vertex as a vector is useful in various tasks such as visualization, classification, and link prediction. However, most hypergraph embedding or learning algorithms reduce multi-way relations to pairwise ones, which turn hypergraphs into graphs and lose a lot of information. Inspired by Laplacian tensors of uniform hypergraphs, we propose in this paper a novel method that incorporates multi-way relations into an optimization problem. We design an objective that is applicable to both uniform and non-uniform hypergraphs with the constraint of having non-negative embedding vectors. For scalability, we apply negative sampling and use constrained stochastic gradient descent to solve the optimization problem. We test our method in a context-aware recommendation task on a real-world dataset. Experimental results show that our method outperforms a few well-known graph and hypergraph embedding methods.