论文标题

HPRA:使用资源分配的超边缘预测

HPRA: Hyperedge Prediction using Resource Allocation

论文作者

Kumar, Tarun, Darwin, K, Parthasarathy, Srinivasan, Ravindran, Balaraman

论文摘要

许多现实世界系统都涉及高阶相互作用,因此需要复杂的模型,例如超图。例如,一篇研究文章可能会有多个合作的作者,因此,共同授权网络最好以超图表表示。在这项工作中,我们专注于超越预测的问题。这个问题在多个领域中具有巨大的应用,例如预测社交网络中的新合作,发现了代谢网络中的新化学反应等。尽管非常重要,但HypereDge预测的问题尚未得到足够的关注,主要是因为其固有的复杂性。在带有$ n $ nodes的图表中,潜在边的数量为$ \ MATHCAL {O}(n^{2})$,而在HyperGraph中,潜在的超增强的数量为$ \ Mathcal {O}(O}(2^{n})$。为了避免在如此巨大的空间中进行搜索,当前的方法通过以下两种方式限制了原始问题。一类算法假设超图为$ k $均匀。但是,许多实际系统不仅限于涉及$ k $组件的交互。因此,这些算法不适合许多现实世界应用。第二类算法需要一组候选的超蛋白质,从中选择了潜在的超蛋白。在没有域知识的情况下,候选集可以具有$ \ Mathcal {o}(2^{n})$可能的Hyperedges,这使此问题很难理解。我们提出了使用资源分配的HPRA -Hyperdege预测,这是同类算法的第一个,它克服了这些问题,并预测了任何基础性的超预交,而无需使用任何候选HyperEdge集。 HPRA是一种基于相似性的方法,可用于资源分配过程的原理。除了恢复缺失的Hyperedges外,我们还证明HPRA可以预测广泛的超图中的未来超息。

Many real-world systems involve higher-order interactions and thus demand complex models such as hypergraphs. For instance, a research article could have multiple collaborating authors, and therefore the co-authorship network is best represented as a hypergraph. In this work, we focus on the problem of hyperedge prediction. This problem has immense applications in multiple domains, such as predicting new collaborations in social networks, discovering new chemical reactions in metabolic networks, etc. Despite having significant importance, the problem of hyperedge prediction hasn't received adequate attention, mainly because of its inherent complexity. In a graph with $n$ nodes the number of potential edges is $\mathcal{O}(n^{2})$, whereas in a hypergraph, the number of potential hyperedges is $\mathcal{O}(2^{n})$. To avoid searching through such a huge space, current methods restrain the original problem in the following two ways. One class of algorithms assume the hypergraphs to be $k$-uniform. However, many real-world systems are not confined only to have interactions involving $k$ components. Thus, these algorithms are not suitable for many real-world applications. The second class of algorithms requires a candidate set of hyperedges from which the potential hyperedges are chosen. In the absence of domain knowledge, the candidate set can have $\mathcal{O}(2^{n})$ possible hyperedges, which makes this problem intractable. We propose HPRA - Hyperedge Prediction using Resource Allocation, the first of its kind algorithm, which overcomes these issues and predicts hyperedges of any cardinality without using any candidate hyperedge set. HPRA is a similarity-based method working on the principles of the resource allocation process. In addition to recovering missing hyperedges, we demonstrate that HPRA can predict future hyperedges in a wide range of hypergraphs.

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