Hyperedge Prediction using Tensor Eigenvalue Decomposition

Abstract

Link prediction in graphs is studied by modeling the dyadic interactions among two nodes. The relationships can be more complex than simple dyadic interactions and could require the user to model super-dyadic associations among nodes. Such interactions can be modeled using a hypergraph, which is a generalization of a graph where a hyperedge can connect more than two nodes.In this work, we consider the problem of hyperedge prediction in a k−uniform hypergraph. We utilize the tensor-based representation of hypergraphs and propose a novel interpretation of the tensor eigenvectors. This is further used to propose a hyperedge prediction algorithm. The proposed algorithm utilizes the Fiedler eigenvector computed using tensor eigenvalue decomposition of hypergraph Laplacian. The Fiedler eigenvector is used to evaluate the construction cost of new hyperedges, which is further utilized to determine the most probable hyperedges to be constructed. The functioning and efficacy of the proposed method are illustrated using some example hypergraphs and a few real datasets. The code for the proposed method is available on this link.

Hyperedge prediction and the statistical mechanisms of higher-order and lower-order interactions in complex networks

“…To make predictions of unobserved hyperedges, these approaches use methods that range from adapted common neighbors or Katz centrality metrics to assess similarity between nodes ( 29 ), to more sophisticated metrics such as resource allocation ( 30 ), or even consider a wide array of topological features of hyperedges to train a binary classifier ( 31 ). Global structural approaches focus on overall properties of the adjacency tensor to predict unobserved hyperedges; these approaches include matrix factorization-based inferential approaches ( 29 ) and spectral approaches ( 32 ). Finally, very recent work uses an inferential approach based on a Poisson formulation of stochastic block models to predict hyperedges of any size ( 17 ).…”