Hyperedge2vec: Distributed Representations for Hyperedges

Data structured in form of overlapping or non-overlapping sets is found in a variety of domains, sometimes explicitly but often subtly. For example, teams, which are of prime importance in social science studies are \enquote{sets of individuals}; \enquote{item sets} in pattern mining are sets; and for various types of analysis in language studies a sentence can be considered as a \enquote{set or bag of words}. Although building models and inference algorithms for structured data has been an important task in the fields of machine learning and statistics, research on \enquote{set-like} data still remains less explored. Relationships between pairs of elements can be modeled as edges in a graph. However, modeling relationships that involve all members of a set, a hyperedge is a more natural representation for the set. In this work, we focus on the problem of embedding hyperedges in a hypergraph (a network of overlapping sets) to a low dimensional vector space. We propose a probabilistic deep-learning based method as well as a tensor-based algebraic model, both of which capture the hypergraph structure in a principled manner without loosing set-level information. Our central focus is to highlight the connection between hypergraphs (topology), tensors (algebra) and probabilistic models. We present a number of interesting baselines, some of which adapt existing node-level embedding models to the hyperedge-level, as well as sequence based language techniques which are adapted for set structured hypergraph topology. The performance is evaluated with a network of social groups and a network of word phrases. Our experiments show that accuracy wise our methods perform similar to those of baselines which are not designed for hypergraphs. Moreover, our tensor based method is quiet efficient as compared to deep-learning based auto-encoder method. We therefore, argue that we have proposed more general methods which are suited for hypergraphs (and therefore also for graphs) while maintaining accuracy and efficiency.