# NS - CUK Seminar: S.T.Nguyen, Review on "Hypergraph Neural Networks", AAAI 2019

26. May 2023
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### NS - CUK Seminar: S.T.Nguyen, Review on "Hypergraph Neural Networks", AAAI 2019

• 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.
• 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.
• 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.