HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Network
This addresses a limitation in modeling multi-way relational data for researchers in graph and hypergraph learning, though it appears incremental as it builds on existing hypergraph neural network frameworks.
The authors tackled the problem of information loss in hypergraph neural networks that reduce hypergraphs to undirected graphs by proposing HyperMagNet, which uses a non-reversible Markov chain and magnetic Laplacian, and demonstrated its effectiveness over graph-reduction methods for node classification.
In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via symmetrized matrix representations, potentially losing important information. We propose an alternative approach to hypergraph neural networks in which the hypergraph is represented as a non-reversible Markov chain. We use this Markov chain to construct a complex Hermitian Laplacian matrix - the magnetic Laplacian - which serves as the input to our proposed hypergraph neural network. We study HyperMagNet for the task of node classification, and demonstrate its effectiveness over graph-reduction based hypergraph neural networks.