Nguyen Thanh Sang
Network Science Lab
Dept. of Artificial Intelligence
The Catholic University of Korea
Hypergraph Neural Networks
--- Yifan Feng, Haoxuan You, Zizhao Zhang, Rongrong Ji, Yue Gao---
+ 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.
+ 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
limits the application of graph convolutional neural networks.
• Propose a hypergraph neural networks (HGNN) framework,
which uses the hypergraph structure for data modeling.
• The complex data correlation is formulated in a hypergraph
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
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:
supervised empirical loss
+ Normalized Ω(f):
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.
• Convolution operation can be further simplified:
• Hyperedge convolution can be formulated by
+ Avoid overfitting:
Hypergraph neural networks analysis
• Multiple hyperedge structure groups are constructed from the complex correlation of the
• 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-
Dilated Aggregation in GCNs
• Applying consecutive pooling layers for dense
• Dilation enlarges the receptive field without loss of
• Dilated k-NN to find dilated neighbors after every
GCN layer and construct a Dilated Graph.
• A dilated graph convolution:
• 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
• 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.
• 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