This document discusses graph convolutional networks (GCNs), which are neural network models for graph-structured data. GCNs aim to learn functions on graphs by preserving the graph's spatial structure and enabling weight sharing. The document outlines the basic components of a GCN, including the adjacency matrix, node features, and application of deep neural network layers. It also notes some challenges with applying convolutions to graphs and discusses approaches like using the graph Fourier transform based on the Laplacian matrix.

2. Introduction
Graph Convolutional Network

3. Introduction
출처 : (Fey et al., CVPR, 2018)

4. Introduction

5. Graph
Graph

6. Graph
Image to graph

7. Graph

8. Graph Convolutional Network
Graph Convolutional Network

9. - Preserve the spatial structure
- Weight sharing
Graph Convolutional Network

10. Adjacency matrix
Node feature
DNN
Ideal algorithm?
[ Naïve Approach ]
1. # of parameters
2. Invariant to node ordering
3. Locality
Graph Convolutional Network

11. Graph Convolutional Network

12. Purpose : graph G=(V,E)에 대해서
Graph-based NN model z = f (X, A) 에서 f 학습하기
Graph Convolutional Network

13. [ Input ]
[ Output ]
[ NN layer]
Graph Convolutional Network

14. [ Layer-wise propagation rule ]
Graph Convolutional Network
With weight matix W(l) of dimension F(l) x F(l+1)

15. [ Layer-wise propagation rule ]
Graph Convolutional Network
symmetric normalized Laplacian matrix form

16. [ Convolution on Graphs? ]
Chebyshev polynomial
Eigen value, vector,
decomposition
Fourier transform
Normalized Graph Laplacian
…….
Graph Convolutional Network
[ Fast Approximate Convolutions on Graphs]
= [ Graph Fourier Transform from Laplacian Matrix ]

17. Graph Convolutional Network
https://raw.githubusercontent.com/wiki/alibaba/euler/images/GCN.png

19. • Kipf, Thomas N., and Max Welling. "Semi-supervised classification with graph convolutional
networks." arXiv preprint arXiv:1609.02907 (2016).