Graph Neural Networks: Architectures, Stability, and Transferability

@article{Ruiz2021GraphNN,
  title={Graph Neural Networks: Architectures, Stability, and Transferability},
  author={Luana Ruiz and Fernando Gama and Alejandro Ribeiro},
  journal={Proceedings of the IEEE},
  year={2021},
  volume={109},
  pages={660-682}
}
Graph neural networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph convolutional filters instead of banks of classical convolutional filters. Otherwise, GNNs operate as CNNs. Filters are composed of pointwise nonlinearities and stacked in layers. It is shown that GNN architectures exhibit equivariance to permutation and… 
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References

SHOWING 1-10 OF 79 REFERENCES
Optimal Wireless Resource Allocation With Random Edge Graph Neural Networks
TLDR
This work introduces the random edge graph neural network (REGNN), which performs convolutions over random graphs formed by the fading interference patterns in the wireless network, and presents an unsupervised model-free primal-dual learning algorithm to train the weights of the REGNN.
Spectral Networks and Locally Connected Networks on Graphs
TLDR
This paper considers possible generalizations of CNNs to signals defined on more general domains without the action of a translation group, and proposes two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian.
Group Invariant Scattering
TLDR
This paper constructs translation-invariant operators on L 2 .R d /, which are Lipschitz-continuous to the action of diffeomorphisms, and extendsScattering operators are extended on L2 .G/, where G is a compact Lie group, and are invariant under theaction of G.
Graph neural networks and the transferability of graph neural networks
  • arXiv:2006.03548v1 [cs.LG], 5 June 2020. [Online]. Available: http://arxiv.org/abs/2006.03548
  • 2006
How Powerful are Graph Neural Networks?
TLDR
This work characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures, and develops a simple architecture that is provably the most expressive among the class of GNNs.
Rating Prediction via Graph Signal Processing
TLDR
New designs for recommendation systems inspired by recent advances in graph signal processing are developed, and it is demonstrated that linear latent factor models can be viewed as bandlimited interpolation algorithms that operate in a frequency domain given by the spectrum of a joint user and item network.
Optimal Graph-Filter Design and Applications to Distributed Linear Network Operators
TLDR
The notion of a node-variant GF, which allows the simultaneous implementation of multiple (regular) GFs in different nodes of the graph, is introduced, which enables the design of more general operators without undermining the locality in implementation.
Semi-Supervised Classification with Graph Convolutional Networks
TLDR
A scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs which outperforms related methods by a significant margin.
Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
TLDR
This work presents a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs.
Spectral Networks and Deep Locally Connected Networks on Graphs
TLDR
This paper considers possible generalizations of CNNs to signals defined on more general domains without the action of a translation group, and proposes two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian.
...
1
2
3
4
5
...