Summary of From Graphs to Hypergraphs: Hypergraph Projection and Its Remediation, by Yanbang Wang et al.
From Graphs to Hypergraphs: Hypergraph Projection and its Remediation
by Yanbang Wang, Jon Kleinberg
First submitted to arxiv on: 16 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Information Retrieval (cs.IR); Social and Information Networks (cs.SI)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores the implications of using a graph to model complex systems with higher-order relationships, rather than a hypergraph. It highlights the limitations of hypergraph projection, which can lead to loss of structural information, and proposes a learning-based approach to recover this lost information. The authors develop an analysis based on graph and set theory to understand the patterns of hyperedges that are affected by projection, and quantify the impossibility of recovering higher-order structures without additional help. They also propose a reconstruction method based on the distribution of hyperedge statistics, which is evaluated on 8 real-world datasets with good performance. This work has implications for protein ranking and link prediction applications. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how to model complex systems that have many connections between different parts. Usually, these connections are represented as a graph, but in this case, the authors use a special kind of graph called a hypergraph. They find that using a regular graph instead can cause important information to be lost. The authors develop a way to understand why this happens and how to get back some of that lost information by training a computer program on the patterns they find. This new approach is tested on real-world data and shows promising results for tasks like ranking proteins and predicting links between them. |
