Hyperedge Prediction using Tensor Eigenvalue Decomposition
This work provides a method for predicting higher-order relationships for researchers working with complex network structures beyond simple graphs, though the impact is not quantified.
This paper addresses the problem of predicting new hyperedges in a k-uniform hypergraph by modeling super-dyadic associations among nodes. It proposes a hyperedge prediction algorithm that leverages a novel interpretation of tensor eigenvectors, specifically the Fiedler eigenvector computed from the tensor eigenvalue decomposition of the hypergraph Laplacian, to evaluate the construction cost of new hyperedges.
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 \textit{Fiedler} eigenvector computed using tensor eigenvalue decomposition of hypergraph Laplacian. The \textit{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 https://github.com/d-maurya/hypred_ tensorEVD