This document summarizes a research paper on hypergraph neural networks. It introduces hypergraphs as a generalization of graphs that allows edges to connect any number of vertices. It then discusses how traditional graph neural networks are limited by only modeling pairwise connections. The paper proposes a hypergraph neural networks framework that uses hypergraph structures to better formulate complex data correlations. Key contributions include a hyperedge convolution operation and experiments showing the framework outperforms traditional graph neural networks on citation network classification and visual object classification tasks by capturing multi-modal data representations.

1. LAB SEMINAR
Nguyen Thanh Sang
Network Science Lab
Dept. of Artificial Intelligence
The Catholic University of Korea
E-mail: sang.ngt99@gmail.com
Hypergraph Neural Networks
--- Yifan Feng, Haoxuan You, Zizhao Zhang, Rongrong Ji, Yue Gao---
2023-05-25

2. Content
s
1
⮚ Paper
▪ Introduction
▪ Problem
▪ Contributions
▪ Framework
▪ Experiment
▪ Conclusion

3. 2
Introduction
Hypergraph
+ A hypergraph is a generalization of a graph in which an edge can join
any number of vertices. In contrast, in an ordinary graph, an edge
connects exactly two vertices.
+ For example, when a large social network with individuals as one
node is built, multiple families are represented.
+ An edge that connects two or more nodes in the hypergraph is
called a hyperedge.

4. 3
Problems
Complicated connections
+ In traditional graph convolutional neural network methods, the
pairwise connections among data are employed.
+ The data structure in real practice could be beyond pairwise
connections and even far more complicated.
 difficult to be modeled by a graph structure.
 the data representation tends to be multi-modal.
+ Traditional graph structure has the limitation to formulate the data
correlation.
 limits the application of graph convolutional neural networks.

5. 4
Contributions
• Propose a hypergraph neural networks (HGNN) framework,
which uses the hypergraph structure for data modeling.
• The complex data correlation is formulated in a hypergraph
structure
 design a hyperedge convolution operation to better exploit the
high-order data correlation for representation learning.
• GCN can be regarded as a special case of HGNN, for which the
edges in simple graph can be regarded as 2-order hyperedges
which connect just two vertices.
• Extensive experiments: on citation network classification and
visual object classification tasks.
 the effectiveness of the proposed HGNN framework.
 better performance of the proposed method when dealing with
multi-modal data.

6. 5
Overview

7. 6
Hypergraph learning statement
• A hypergraph is defined as G = (V, E,W), which includes a vertex set V, a hyperedge set E.
• Each hyperedge is assigned with a weight by W, a diagonal matrix of edge weights.
• The hypergraph G can be denoted by a |V| × |E| incidence matrix H:
• Degree of v:
• Degree of edge:
• Node classification:
regularize Ω(f)
hypergraph Laplacian
supervised empirical loss
+ Normalized Ω(f):

8. 7
Spectral convolution on hypergraph
• Fourier transform for a signal in hypergraph is defined as
• spectral convolution of signal x and filter g can be denoted as
• Fourier coefficients:
• The computation cost in forward and inverse Fourier transform is high.
 Use K:
• Convolution operation can be further simplified:
• Hyperedge convolution can be formulated by
+ Avoid overfitting:

9. 8
Hypergraph neural networks analysis
• Multiple hyperedge structure groups are constructed from the complex correlation of the
multi-modality datasets.
• The hypergraph adjacent matrix H and the node feature are fed into the HGNN to get the
node output labels.
• HGNN layer can efficiently extract the high-order correlation on hypergraph by the node-
edge-node transform

10. 9
Dilated Aggregation in GCNs
• Applying consecutive pooling layers for dense
prediction tasks.
• Dilation enlarges the receptive field without loss of
resolution.
• Dilated k-NN to find dilated neighbors after every
GCN layer and construct a Dilated Graph.
• A dilated graph convolution:

11. 10
Architectures
• PlainGCN: consists of a PlainGCN backbone block, a fusion block, and a MLP prediction block. No
skip connections are used here.
• ResGCN: adding dynamic dilated k-NN and residual graph connections to PlainGCN. These
connections between all GCN layers in the GCN backbone block do not increase the number of
parameters.
• DenseGCN. built by adding dynamic dilated k-NN and dense graph connections to the PlainGCN.
A dense graph connections are created by concatenating all the intermediate graph
representations from previous layers.

12. 11
Experiments

13. 12
Conclusions
• A framework of hypergraph neural networks (HGNN) which generalizes the convolution
operation to the hypergraph learning process.
• The convolution on spectral domain is conducted with hypergraph Laplacian and further
approximated by truncated chebyshev polynomials.
• HGNN is able to handle the complex and high-order correlations through the hypergraph
structure for representation learning compared with traditional graph.
• HGNN is able to take complex data correlation into representation learning and thus lead to
potential wide applications in many tasks, such as visual recognition, retrieval and data
classification.

14. 13
Thank you!