Hypergraph Echo State Network

A hypergraph as a generalization of graphs records higher-order interactions among nodes, yields a more flexible network model, and allows non-linear features for a group of nodes. In this article, we propose a hypergraph echo state network (HypergraphESN) as a generalization of graph echo state network (GraphESN) designed for efficient processing of hypergraph-structured data, derive convergence conditions for the algorithm, and discuss its versatility in comparison to GraphESN. The numerical experiments on the binary classification tasks demonstrate that HypergraphESN exhibits comparable or superior accuracy performance to GraphESN for hypergraph-structured data, and accuracy increases if more higher-order interactions in a network are identified.