How Much and When Do We Need Higher-order Informationin Hypergraphs? A Case Study on Hyperedge Prediction

How Much and When Do We Need Higher-order Information in Hypergraphs? A Case Study on Hyperedge Prediction

Abstract.

Hypergraphs provide a natural way of representing group relations, whose complexity motivates an extensive array of prior work to adopt some form of abstraction and simplification of higher-order interactions. However, the following question has yet to be addressed: How much abstraction of group interactions is sufficient in solving a hypergraph task, and how different such results become across datasets? This question, if properly answered, provides a useful engineering guideline on how to trade off between complexity and accuracy of solving a downstream task. To this end, we propose a method of incrementally representing group interactions using a notion of -projected graph whose accumulation contains information on up to -way interactions, and quantify the accuracy of solving a task as grows for various datasets. As a downstream task, we consider hyperedge prediction, an extension of link prediction, which is a canonical task for evaluating graph models. Through experiments on 15 real-world datasets, we draw the following messages: (a) Diminishing returns: small is enough to achieve accuracy comparable with near-perfect approximations, (b) Troubleshooter: as the task becomes more challenging, larger brings more benefit, and (c) Irreducibility: datasets whose pairwise interactions do not tell much about higher-order interactions lose much accuracy when reduced to pairwise abstractions.

hypergraphs, hyperedge prediction, link prediction, graph mining
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References

Footnotes

  1. journalyear: 2020
  2. copyright: iw3c2w3
  3. conference: Proceedings of The Web Conference 2020; April 20–24, 2020; Taipei, Taiwan
  4. booktitle: Proceedings of The Web Conference 2020 (WWW ’20), April 20–24, 2020, Taipei, Taiwan
  5. price:
  6. doi: 10.1145/3366423.3380016
  7. isbn: 978-1-4503-7023-3/20/04
  8. ccs: Information systems Data mining
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