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[DL Hacks]Semi-Supervised Classification with Graph Convolutional Networks
- 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
•
- 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
- 11. Layer-Wise Linear Model (2)
• !" + $%
&
'($%
&
' → *$%
&
' +(*$%
&
'
• +( = ( + !"
• *$-- = Σ/
+(-/
• (5)
• 0 ∈ ℝ"×4
• Θ ∈ ℝ4×6
• Z ∈ ℝ"×6
10
- 14. •
• Ex. [Zhu et al., 2003]
•
•
• skip-gram
• Ex. DeepWalk [Perozzi et al., 2014]
• random walk
•
13