Supervised Hypergraph Reconstruction

TL;DR

This paper introduces a supervised hypergraph reconstruction method that accurately reconstructs hypergraphs from their projections, addressing a common issue in complex systems analysis and outperforming existing baselines.

Contribution

The paper formulates the novel task of supervised hypergraph reconstruction and proposes an effective framework with sampling and classification modules, validated by extensive experiments.

Findings

Outperforms all baselines by an order of magnitude in accuracy.

Effectively narrows search space for hyperedge candidates.

Validates approach with extensive experiments on hard datasets.

Abstract

We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of their projections (with dyadic edges). To understand this issue, we first establish a theoretical framework to characterize this issue's implications and worst-case scenarios. The analysis motivates our formulation of the new task, supervised hypergraph reconstruction: reconstructing a real-world hypergraph from its projected graph, with the help of some existing knowledge of the application domain. To reconstruct hypergraph data, we start by analyzing hyperedge distributions in the projection, based on which we create a framework containing two modules: (1) to handle the enormous search space of potential hyperedges, we design a sampling strategy with efficacy guarantees that significantly narrows the space to a smaller set of candidates; (2) to identify hyperedges from the candidates, we further design a hyperedge classifier in two well-working variants that capture structural features in the projection. Extensive experiments validate our claims, approach, and extensions. Remarkably, our approach outperforms all baselines by an order of magnitude in accuracy on hard datasets. Our code and data can be downloaded from bit.ly/SHyRe.