Let There be Direction in Hypergraph Neural Networks
Abstract: Hypergraphs are a powerful abstraction for modeling high-order interactions between a set of entities of interest and have been attracting a growing interest in the graph-learning literature. In particular, directed hypegraphs are crucial in their capability of representing real-world phenomena involving group relations where two sets of elements affect one another in an asymmetric way. Despite such a vast potential, an established solution to tackle graph-learning tasks on directed hypergraphs is still lacking. For this reason, in this paper we introduce the Generalized Directed Hypergraph Neural Network (GeDi-HNN), the first spectral-based Hypergraph Neural Network (HNN) capable of seamlessly handling hypergraphs with both directed and undirected hyperedges. GeDi-HNN relies on a graph-convolution operator which is built on top of the Generalized Directed Laplacian} $\vec{L}_N$, a novel complex-valued Hermitian matrix which we introduce in this paper. We prove that $\vec L_N$ generalizes many previously-proposed Laplacian matrices to directed hypergraphs while enjoying several desirable spectral properties. Extensive computational experiments against state-of-the-art methods on real-world and synthetically-generated datasets demonstrate the efficacy of our proposed HNN. Thanks to effectively leveraging the directional information contained in these datasets, GeDi-HNN achieves a relative-percentage-difference improvement of 7% on average (with a maximum improvement of 23.19%) on the real-world datasets and of 65.3% on average on the synthetic ones.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: We discovered a mistake in Equation 7. Instead of writing $\vec L_N := I - \vec Q_N$, we wrote $\vec L_N := - \vec Q_N$.
Assigned Action Editor: ~Giannis_Nikolentzos1
Submission Number: 2807
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