# Co-clustering Vertices and Hyperedges via Spectral Hypergraph Partitioning

arXiv: https://arxiv.org/abs/2102.10169 · HTML: https://mlsanity.com/paper/2102.10169/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 19 Feb 2021.

## Builds on (most cited first, 10 of 10)

- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Random Walks on Hypergraphs with Edge-Dependent Vertex Weights](https://mlsanity.com/paper/1905.08287/) (2019)
- [REGAL: Representation Learning-based Graph Alignment](https://mlsanity.com/paper/1802.06257/) (2018)
- [Inhomogeneous Hypergraph Clustering with Applications](https://mlsanity.com/paper/1709.01249/) (2017)
- [Hermitian matrices for clustering directed graphs: insights and applications](https://mlsanity.com/paper/1908.02096/) (2019)
- [Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration](https://mlsanity.com/paper/1909.06503/) (2019)
- [Recent Advances in Graph Partitioning](https://mlsanity.com/paper/1311.3144/) (2013)
- [Hypergraph Random Walks, Laplacians, and Clustering](https://mlsanity.com/paper/2006.16377/) (2020)
- [Analysis of Network Clustering Algorithms and Cluster Quality Metrics at Scale](https://mlsanity.com/paper/1605.05797/) (2016)
- [Triangular Alignment (TAME): A Tensor-based Approach for Higher-order Network Alignment](https://mlsanity.com/paper/1510.06482/) (2015)

## Built on by (most cited first, 3 of 3)

- [Free Energy Node Embedding via Generalized Skip-gram with Negative Sampling](https://mlsanity.com/paper/2105.09182/) (2021)
- [Hypergraphs with Edge-Dependent Vertex Weights: p-Laplacians and Spectral Clustering](https://mlsanity.com/paper/2208.07457/) (2022)
- [Hypergraphs with Edge-Dependent Vertex Weights: Spectral Clustering based on the 1-Laplacian](https://mlsanity.com/paper/2305.00462/) (2023)

## Abstract (arXiv)

We propose a novel method to co-cluster the vertices and hyperedges of hypergraphs with edge-dependent vertex weights (EDVWs). In this hypergraph model, the contribution of every vertex to each of its incident hyperedges is represented through an edge-dependent weight, conferring the model higher expressivity than the classical hypergraph. In our method, we leverage random walks with EDVWs to construct a hypergraph Laplacian and use its spectral properties to embed vertices and hyperedges in a common space. We then cluster these embeddings to obtain our proposed co-clustering method, of particular relevance in applications requiring the simultaneous clustering of data entities and features. Numerical experiments using real-world data demonstrate the effectiveness of our proposed approach in comparison with state-of-the-art alternatives.