# Hyperedge Representations with Hypergraph Wavelets: Applications to Spatial Transcriptomics

arXiv: https://arxiv.org/abs/2409.09469 · HTML: https://mlsanity.com/paper/2409.09469/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 14 Sep 2024.

## Builds on (most cited first, 11 of 11)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Introducing Hypergraph Signal Processing: Theoretical Foundation and Practical Applications](https://mlsanity.com/paper/1907.09203/) (2019)
- [Assessing Neural Network Representations During Training Using Noise-Resilient Diffusion Spectral Entropy](https://mlsanity.com/paper/2312.04823/) (2023)
- [Learnable Filters for Geometric Scattering Modules](https://mlsanity.com/paper/2208.07458/) (2022)

## Built on by (most cited first, 4 of 4)

- [Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds](https://mlsanity.com/paper/2410.12779/) (2024)
- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [InfoGain Wavelets: Furthering the Design of Graph Diffusion Wavelets](https://mlsanity.com/paper/2504.08802/) (2025)
- [STAGED: A Multi-Agent Neural Network for Learning Cellular Interaction Dynamics](https://mlsanity.com/paper/2507.11660/) (2025)

## Abstract (arXiv)

In many data-driven applications, higher-order relationships among multiple objects are essential in capturing complex interactions. Hypergraphs, which generalize graphs by allowing edges to connect any number of nodes, provide a flexible and powerful framework for modeling such higher-order relationships. In this work, we introduce hypergraph diffusion wavelets and describe their favorable spectral and spatial properties. We demonstrate their utility for biomedical discovery in spatially resolved transcriptomics by applying the method to represent disease-relevant cellular niches for Alzheimer's disease.