基于张量特征值分解的超边缘预测
Hyperedge Prediction using Tensor Eigenvalue Decomposition
摘要：
通过对图中节点间的二元交互进行建模，研究了图中的链接预测。这些关系可能比简单的二元交互更复杂，并且可能需要用户对节点之间的超级二元关联进行建模。这种交互可以使用超图来建模，超图是超边可以连接两个以上节点的图的推广。本文研究了$k-$一致超图的超边预测问题。我们利用基于张量的超图表示，并提出了一种新的解释张量特征向量。这进一步被用来提出一个超边缘预测算法。该算法利用超图Laplacian的张量特征值分解计算的\textit{Fiedler}特征向量。利用\textit{Fiedler}特征向量估计新超边的构造代价，进而确定待构造的最可能超边.所提出的方法的功能和有效性说明使用一些例子超图和一些真实的数据集。所提出的方法的代码可在https://github.com/d-maurya/hypred_ tensorEVD上获得
英文摘要：
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
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
