Learning over Families of Sets -- Hypergraph Representation Learning for Higher Order Tasks
This addresses the limitation of existing hypergraph methods in handling non-uniform hypergraphs, which is crucial for domains with higher-order interactions beyond pairwise relationships.
The paper tackles the problem of learning representations for hyperedges in non-uniform hypergraphs, where relationships involve variable-sized sets of entities, by developing a hypergraph neural network that preserves local-isomorphism and permutation invariance. It demonstrates consistent, significant improvements in accuracy on real-world datasets compared to state-of-the-art models.
Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise interactions. In such cases, the relationships in the data are better represented as hyperedges (set of entities) of a non-uniform hypergraph. While there have been works on principled methods for learning representations of nodes of a hypergraph, these approaches are limited in their applicability to tasks on non-uniform hypergraphs (hyperedges with different cardinalities). In this work, we exploit the incidence structure to develop a hypergraph neural network to learn provably expressive representations of variable sized hyperedges which preserve local-isomorphism in the line graph of the hypergraph, while also being invariant to permutations of its constituent vertices. Specifically, for a given vertex set, we propose frameworks for (1) hyperedge classification and (2) variable sized expansion of partially observed hyperedges which captures the higher order interactions among vertices and hyperedges. We evaluate performance on multiple real-world hypergraph datasets and demonstrate consistent, significant improvement in accuracy, over state-of-the-art models.