# Community Detection in General Hypergraph via Graph Embedding

arXiv: https://arxiv.org/abs/2103.15035 · HTML: https://mlsanity.com/paper/2103.15035/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 28 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [The landscape of the spiked tensor model](https://mlsanity.com/paper/1711.05424/) (2017)
- [Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decomposition](https://mlsanity.com/paper/2002.04457/) (2020)
- [Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration](https://mlsanity.com/paper/1909.06503/) (2019)
- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [Consistency of Spectral Hypergraph Partitioning under Planted Partition Model](https://mlsanity.com/paper/1505.01582/) (2015)
- [Coauthorship and Citation Networks for Statisticians](https://mlsanity.com/paper/1410.2840/) (2014)
- [Network Cross-Validation for Determining the Number of Communities in Network Data](https://mlsanity.com/paper/1411.1715/) (2014)
- [Hypergraph Spectral Clustering in the Weighted Stochastic Block Model](https://mlsanity.com/paper/1805.08956/) (2018)
- [Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squares](https://mlsanity.com/paper/1705.02973/) (2017)
- [Uniform Hypergraph Partitioning: Provable Tensor Methods and Sampling Techniques](https://mlsanity.com/paper/1602.06516/) (2016)
- [On the Minimax Misclassification Ratio of Hypergraph Community Detection](https://mlsanity.com/paper/1802.00926/) (2018)
- [Convex Relaxation Methods for Community Detection](https://mlsanity.com/paper/1810.00315/) (2018)
- [Probabilistic community detection with unknown number of communities](https://mlsanity.com/paper/1602.08062/) (2016)
- [Individualized Multi-directional Variable Selection](https://mlsanity.com/paper/1709.05062/) (2017)
- [Optimal Bayesian Estimation for Random Dot Product Graphs](https://mlsanity.com/paper/1904.12070/) (2019)
- [Hypergraph Clustering: A Modularity Maximization Approach](https://mlsanity.com/paper/1812.10869/) (2018)

## Built on by (most cited first, 12 of 12)

- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Model](https://mlsanity.com/paper/2112.11671/) (2021)
- [Sparse random hypergraphs: Non-backtracking spectra and community detection](https://mlsanity.com/paper/2203.07346/) (2022)
- [Community Detection in the Hypergraph SBM: Exact Recovery Given the Similarity Matrix](https://mlsanity.com/paper/2208.12227/) (2022)
- [Multilayer hypergraph clustering using the aggregate similarity matrix](https://mlsanity.com/paper/2301.11657/) (2023)
- [Optimal and exact recovery on the general nonuniform Hypergraph Stochastic Block Model](https://mlsanity.com/paper/2304.13139/) (2023)
- [Community detection in censored hypergraph](https://mlsanity.com/paper/2111.03179/) (2021)
- [Tensorized Hypergraph Neural Networks](https://mlsanity.com/paper/2306.02560/) (2023)
- [Scalable tensor methods for nonuniform hypergraphs](https://mlsanity.com/paper/2306.17825/) (2023)
- [Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model](https://mlsanity.com/paper/2307.00575/) (2023)
- [Efficient Estimation for Longitudinal Networks via Adaptive Merging](https://mlsanity.com/paper/2211.07866/) (2022)
- [Network-based Neighborhood regression](https://mlsanity.com/paper/2407.04104/) (2024)

## Abstract (arXiv)

Conventional network data has largely focused on pairwise interactions between two entities, yet multi-way interactions among multiple entities have been frequently observed in real-life hypergraph networks. In this article, we propose a novel method for detecting community structure in general hypergraph networks, uniform or non-uniform. The proposed method introduces a null vertex to augment a non-uniform hypergraph into a uniform multi-hypergraph, and then embeds the multi-hypergraph in a low-dimensional vector space such that vertices within the same community are close to each other. The resultant optimization task can be efficiently tackled by an alternative updating scheme. The asymptotic consistencies of the proposed method are established in terms of both community detection and hypergraph estimation, which are also supported by numerical experiments on some synthetic and real-life hypergraph networks.