This document discusses graph convolutional networks (GCNs), which use graph convolutions to perform semi-supervised learning on graphs. GCNs apply convolutional filters directly on graphs by using a graph Laplacian matrix to capture information from a node's local neighborhood. The document outlines how GCNs perform layer-wise linear models using a graph convolution theorem to aggregate features from neighboring nodes. An example application to a citation network demonstrates how GCNs can be used for semi-supervised node classification tasks on graph-structured data.

1. Semi-Supervised Classification with
Graph Convolutional Networks
M2
0

2. •
• ICLR 2017
•
•
•
1

3. •
(Graph Convolutional Network)
• Graph Convolution
•
• Graph Convolutional Network
•
•
2

4. Graph Convolutional Network ( )
A
•
•
!" = " + %& (A: , %&: )
'()) = Σ+
!")+
,:
.(0) ∈ ℝ& × 5 : l
3

5. !(#) ∈ ℝ' × ) !(#*+) ∈ ℝ' × ,
N
4
: Shuman et al. 2013

6. Spectral Graph Convolutions (1)
N ( ) (1)
• x:
• ! ∈ ℝ$
( )
• U:
• % = '$ − )*
+
,-)*
+
, = .Λ.0
• 12 = 3451 6
• 6 ∈ ℝ$
(1)
5
•
• U 7 89
• U
•

7. 1
•
• L:
• A: ( )
• D:
6

8. 2
…
↓
Convolution Theorem ( Fourier )
↓
Graph Graph Fourier
Convolution Theorem
Convolution Theorem
!" ∗ $ = &" ⊙ ($
&" : f Fourier
* :
⊙:
Graph Convolutional Network LT ( DL_Hacks )
https://www.slideshare.net/DeepLearningJP2016/graph-convolutional-network-lt
7

9. Spectral Graph Convolutions (2)
• !" Λ [Hammond et al. 2011]
• $Λ$% & = $Λ&$%
• (′ ∈ ℝ,
• -Λ =
.
/012
Λ − 45 (7: 9 )
• ;9 =
.
/012
9 − 45
(2)
(3)
• (3) k-hop ( )
8

10. Layer-Wise Linear Model (1)
GCN
• (3) K = 1, !"#$ = 2
•
• ( )
• !"#$ NN
(4)
• (4) % = %'
(
= −%*
(
•
(5)
9

11. Layer-Wise Linear Model (2)
• !" + $%
&
'($%
&
' → *$%
&
' +(*$%
&
'
• +( = ( + !"
• *$-- = Σ/
+(-/
• (5)
• 0 ∈ ℝ"×4
• Θ ∈ ℝ4×6
• Z ∈ ℝ"×6
10

12. Graph Convolutional Network ( )
A
•
•
!" = " + %& (A: , %&: )
'()) = Σ+
!")+
,:
.(0) ∈ ℝ& × 5 : l
11

13. GCN
•
•
Karate Club [Brandes et al. 2008]
•
• ( )
•
•
•
12

14. •
• Ex. [Zhu et al., 2003]
•
•
• skip-gram
• Ex. DeepWalk [Perozzi et al., 2014]
• random walk
•
13

15. GCN
14
[X1 ]
[X2 ]
[X3 ]
[X4 ]
[Z1 ]
[Z2 ]
[Z3 ]
[Z4 ]
4 * K 4 * Q
• 1, 4 Loss ( )
•
2 GCN
Loss

16. Citation Network
• Citation Network
• bag-of-words
•
• Label rate
15

17. 16

18. •
•
•
•
•
• https://www.inference.vc/how-powerful-are-graph-convolutions-review-of-
kipf-welling-2016-2/
•
•
17

19. • Graph Convolutional Network
• Graph Convolution
•
•
• GCN
•
•
18