# Hypergraph Modeling via Spectral Embedding Connection: Hypergraph Cut, Weighted Kernel k-means, and Heat Kernel

arXiv: https://arxiv.org/abs/2203.09888 · HTML: https://mlsanity.com/paper/2203.09888/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 18 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited](https://mlsanity.com/paper/1312.5179/) (2013)
- [Inhomogeneous Hypergraph Clustering with Applications](https://mlsanity.com/paper/1709.01249/) (2017)
- [Submodular Hypergraphs: p-Laplacians, Cheeger Inequalities and Spectral Clustering](https://mlsanity.com/paper/1803.03833/) (2018)
- [Hypergraph Cuts with General Splitting Functions](https://mlsanity.com/paper/2001.02817/) (2020)
- [Uniform Hypergraph Partitioning: Provable Tensor Methods and Sampling Techniques](https://mlsanity.com/paper/1602.06516/) (2016)
- [Cheeger Inequalities for Submodular Transformations](https://mlsanity.com/paper/1708.08781/) (2017)
- [Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning](https://mlsanity.com/paper/2011.07752/) (2020)
- [Hypergraph p-Laplacian: A Differential Geometry View](https://mlsanity.com/paper/1711.08171/) (2017)
- [Hypergraph Markov Operators, Eigenvalues and Approximation Algorithms](https://mlsanity.com/paper/1408.2425/) (2014)
- [Finding Cheeger Cuts in Hypergraphs via Heat Equation](https://mlsanity.com/paper/1809.04396/) (2018)

## Built on by (most cited first, 1 of 1)

- [Inferring Network Evolutionary History via Structure-State Coupled Learning](https://mlsanity.com/paper/2601.02121/) (2026)

## Abstract (arXiv)

We propose a theoretical framework of multi-way similarity to model real-valued data into hypergraphs for clustering via spectral embedding. For graph cut based spectral clustering, it is common to model real-valued data into graph by modeling pairwise similarities using kernel function. This is because the kernel function has a theoretical connection to the graph cut. For problems where using multi-way similarities are more suitable than pairwise ones, it is natural to model as a hypergraph, which is generalization of a graph. However, although the hypergraph cut is well-studied, there is not yet established a hypergraph cut based framework to model multi-way similarity. In this paper, we formulate multi-way similarities by exploiting the theoretical foundation of kernel function. We show a theoretical connection between our formulation and hypergraph cut in two ways, generalizing both weighted kernel k-means and the heat kernel, by which we justify our formulation. We also provide a fast algorithm for spectral clustering. Our algorithm empirically shows better performance than existing graph and other heuristic modeling methods.