# A Simple Hypergraph Kernel Convolution based on Discounted Markov Diffusion Process

arXiv: https://arxiv.org/abs/2210.16884 · HTML: https://mlsanity.com/paper/2210.16884/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 30 Oct 2022.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Interpolated Convolutional Networks for 3D Point Cloud Understanding](https://mlsanity.com/paper/1908.04512/) (2019)
- [Be More with Less: Hypergraph Attention Networks for Inductive Text Classification](https://mlsanity.com/paper/2011.00387/) (2020)
- [On Provable Benefits of Depth in Training Graph Convolutional Networks](https://mlsanity.com/paper/2110.15174/) (2021)
- [HyperSAGE: Generalizing Inductive Representation Learning on Hypergraphs](https://mlsanity.com/paper/2010.04558/) (2020)
- [Random Walks on Hypergraphs with Edge-Dependent Vertex Weights](https://mlsanity.com/paper/1905.08287/) (2019)
- [Preventing Over-Smoothing for Hypergraph Neural Networks](https://mlsanity.com/paper/2203.17159/) (2022)
- [Fine-Tuning Graph Neural Networks via Graph Topology induced Optimal Transport](https://mlsanity.com/paper/2203.10453/) (2022)
- [Learnable Hypergraph Laplacian for Hypergraph Learning](https://mlsanity.com/paper/2106.05701/) (2021)
- [Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs](https://mlsanity.com/paper/2203.16939/) (2022)
- [Quadratic Decomposable Submodular Function Minimization: Theory and Practice (Computation and Analysis of PageRank over Hypergraphs)](https://mlsanity.com/paper/1902.10132/) (2019)
- [Random walks and community detection in hypergraphs](https://mlsanity.com/paper/2010.14355/) (2020)
- [Diversified Multiscale Graph Learning with Graph Self-Correction](https://mlsanity.com/paper/2103.09754/) (2021)

## Built on by (most cited first, 2 of 2)

- [Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passing](https://mlsanity.com/paper/2604.10955/) (2026)
- [Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusion](https://mlsanity.com/paper/2405.14286/) (2024)

## Abstract (arXiv)

Kernels on discrete structures evaluate pairwise similarities between objects which capture semantics and inherent topology information. Existing kernels on discrete structures are only developed by topology information(such as adjacency matrix of graphs), without considering original attributes of objects. This paper proposes a two-phase paradigm to aggregate comprehensive information on discrete structures leading to a Discount Markov Diffusion Learnable Kernel (DMDLK). Specifically, based on the underlying projection of DMDLK, we design a Simple Hypergraph Kernel Convolution (SHKC) for hidden representation of vertices. SHKC can adjust diffusion steps rather than stacking convolution layers to aggregate information from long-range neighborhoods which prevents over-smoothing issues of existing hypergraph convolutions. Moreover, we utilize the uniform stability bound theorem in transductive learning to analyze critical factors for the effectiveness and generalization ability of SHKC from a theoretical perspective. The experimental results on several benchmark datasets for node classification tasks verified the superior performance of SHKC over state-of-the-art methods.