Hypergraph Neural Networks
01 Background
Introduced in the paper Yifan Feng et. al., 2018, Hypergraph Neural Networks.It’s aim is to improve on traditional Graph Convolutional Networks, specifically
Related Papers
- [Kipf, Thomas N, and Max Welling, ICLR 2017. Semi-supervised classification with graph convolutional networks].
Questions to answer?
- What is a hypergraph and its comparison to a simple traditional graph
Sources?
02 Hypergraph Neural Network
Hypergraph Neural Network
Edge in simple graph, connect exactly in 2 vertices Hyperedge in hypergraph, allows any numer of vertices to join in.
Hypergraph better expressive ability Examples, Group relationship in wechat more than just pairwise relationhsip, but high order relationship.
Paper: [Kipf, Thomas N, and Max Welling, ICLR 2017. Semi-supervised classification with graph convolutional networks]
Background
- Graph based convolutional neural networks ave shown superiority to traditional neural networks
- Traditional graph convolutional neural network methods face 2 shortcomings:
- Data structure could be more complex than pairwise
- data representation tends to be multimodal
- Hypergraph learning is first introduced in 2007
- (Huang et al. 2010) Used the hypergraph structure to model image relationship
- (Gao et al introduced hypergraph structure to assign weights for different sub-hypergraphs which corresponds to different modalites.
- Traditional hypergraph learning methods suffer from high computation and storage class
Main idea:
- introduce the hypergraph structure to GCNs, and propose efficient hypergraph Build a graph convolution network using hypergraph structure
- how to describe a hypergraph?
- what is teh convolution in hypergraph?
- how to do graph convolution learning in hypergraph?
Mathematical Description of Hypergraphs Description Incident Matrrx Vertex Degree Vertex degree edge degree edge degree matrix graph signal laplacian matrix
What is convolution in hypergraph, convolution operation and fourier transform
- 卷积运算
- 傅立叶变换
- 卷积定理
How to