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Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek...
Transcript of Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek...
![Page 1: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/1.jpg)
Graph Based Semi-supervised Learning
Aydın Gerek
Marmara University
May 26th, 2018
Aydın Gerek Graph Based Semi-supervised Learning
![Page 2: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/2.jpg)
Learning Paradigms
Supervised Learning
Unsupervised LearningSemi-supervised Learning
InductiveTransductive
Aydın Gerek Graph Based Semi-supervised Learning
![Page 3: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/3.jpg)
Learning Paradigms
Supervised LearningUnsupervised Learning
Semi-supervised Learning
InductiveTransductive
Aydın Gerek Graph Based Semi-supervised Learning
![Page 4: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/4.jpg)
Learning Paradigms
Supervised LearningUnsupervised LearningSemi-supervised Learning
InductiveTransductive
Aydın Gerek Graph Based Semi-supervised Learning
![Page 5: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/5.jpg)
Learning Paradigms
Supervised LearningUnsupervised LearningSemi-supervised Learning
Inductive
Transductive
Aydın Gerek Graph Based Semi-supervised Learning
![Page 6: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/6.jpg)
Learning Paradigms
Supervised LearningUnsupervised LearningSemi-supervised Learning
InductiveTransductive
Aydın Gerek Graph Based Semi-supervised Learning
![Page 7: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/7.jpg)
Graphs
V = set of vertices
E = set of edges
Auv =
{1 (u, v) ∈ E0 (u, v) /∈ E
Duv =
{∑w Auw u = v
0 u 6= v
∆ = D − A L = D−1/2∆D−1/2
Aydın Gerek Graph Based Semi-supervised Learning
![Page 8: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/8.jpg)
Graphs
V = set of vertices E = set of edges
Auv =
{1 (u, v) ∈ E0 (u, v) /∈ E
Duv =
{∑w Auw u = v
0 u 6= v
∆ = D − A L = D−1/2∆D−1/2
Aydın Gerek Graph Based Semi-supervised Learning
![Page 9: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/9.jpg)
Graphs
V = set of vertices E = set of edges
Auv =
{1 (u, v) ∈ E0 (u, v) /∈ E
Duv =
{∑w Auw u = v
0 u 6= v
∆ = D − A L = D−1/2∆D−1/2
Aydın Gerek Graph Based Semi-supervised Learning
![Page 10: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/10.jpg)
Graphs
V = set of vertices E = set of edges
Auv =
{wuv (u, v) ∈ E0 (u, v) /∈ E
Duv =
{∑w Auw u = v
0 u 6= v
∆ = D − A L = D−1/2∆D−1/2
Aydın Gerek Graph Based Semi-supervised Learning
![Page 11: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/11.jpg)
Graphs
V = set of vertices E = set of edges
Auv =
{wuv (u, v) ∈ E0 (u, v) /∈ E
Duv =
{∑w Auw u = v
0 u 6= v
∆ = D − A L = D−1/2∆D−1/2
Aydın Gerek Graph Based Semi-supervised Learning
![Page 12: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/12.jpg)
Graphs
V = set of vertices E = set of edges
Auv =
{wuv (u, v) ∈ E0 (u, v) /∈ E
Duv =
{∑w Auw u = v
0 u 6= v
∆ = D − A
L = D−1/2∆D−1/2
Aydın Gerek Graph Based Semi-supervised Learning
![Page 13: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/13.jpg)
Graphs
V = set of vertices E = set of edges
Auv =
{wuv (u, v) ∈ E0 (u, v) /∈ E
Duv =
{∑w Auw u = v
0 u 6= v
∆ = D − A L = D−1/2∆D−1/2
Aydın Gerek Graph Based Semi-supervised Learning
![Page 14: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/14.jpg)
Gaussian Random Fields (GRF) (Zhu et al., 2003)
also known as Label Propagation
arg minY∈Rn×|Y|
∑`∈Y
∑(u,v)∈E
Auv (Yu` − Yv`)2
= arg minY∈Rn×|Y|
∑`∈Y
Y`T
∆Y`
s.t. Yu` = Yu`,∀` ∈ Y, ∀ labeled u
Y (t+1)v` ←
∑(u,v)∈E Auv Y (t)
u`
Y (t+1) ← D−1AY (t)
Harmonic Property: node = average of neighbors
Aydın Gerek Graph Based Semi-supervised Learning
![Page 15: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/15.jpg)
Gaussian Random Fields (GRF) (Zhu et al., 2003)
also known as Label Propagation
arg minY∈Rn×|Y|
∑`∈Y
∑(u,v)∈E
Auv (Yu` − Yv`)2
= arg minY∈Rn×|Y|
∑`∈Y
Y`T
∆Y`
s.t. Yu` = Yu`,∀` ∈ Y, ∀ labeled u
Y (t+1)v` ←
∑(u,v)∈E Auv Y (t)
u`
Y (t+1) ← D−1AY (t)
Harmonic Property: node = average of neighbors
Aydın Gerek Graph Based Semi-supervised Learning
![Page 16: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/16.jpg)
Gaussian Random Fields (GRF) (Zhu et al., 2003)
also known as Label Propagation
arg minY∈Rn×|Y|
∑`∈Y
∑(u,v)∈E
Auv (Yu` − Yv`)2 = arg min
Y∈Rn×|Y|
∑`∈Y
Y`T
∆Y`
s.t. Yu` = Yu`,∀` ∈ Y, ∀ labeled u
Y (t+1)v` ←
∑(u,v)∈E Auv Y (t)
u`
Y (t+1) ← D−1AY (t)
Harmonic Property: node = average of neighbors
Aydın Gerek Graph Based Semi-supervised Learning
![Page 17: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/17.jpg)
Gaussian Random Fields (GRF) (Zhu et al., 2003)
also known as Label Propagation
arg minY∈Rn×|Y|
∑`∈Y
∑(u,v)∈E
Auv (Yu` − Yv`)2 = arg min
Y∈Rn×|Y|
∑`∈Y
Y`T
∆Y`
s.t. Yu` = Yu`,∀` ∈ Y, ∀ labeled u
Y (t+1)v` ←
∑(u,v)∈E Auv Y (t)
u`∑(u,v)∈E Auv
Y (t+1) ← D−1AY (t)
Harmonic Property: node = average of neighbors
Aydın Gerek Graph Based Semi-supervised Learning
![Page 18: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/18.jpg)
Gaussian Random Fields (GRF) (Zhu et al., 2003)
also known as Label Propagation
arg minY∈Rn×|Y|
∑`∈Y
∑(u,v)∈E
Auv (Yu` − Yv`)2 = arg min
Y∈Rn×|Y|
∑`∈Y
Y`T
∆Y`
s.t. Yu` = Yu`,∀` ∈ Y, ∀ labeled u
Y (t+1)v` ←
∑(u,v)∈E Auv Y (t)
u`
Dvv
Y (t+1) ← D−1AY (t)
Harmonic Property: node = average of neighbors
Aydın Gerek Graph Based Semi-supervised Learning
![Page 19: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/19.jpg)
Gaussian Random Fields (GRF) (Zhu et al., 2003)
also known as Label Propagation
arg minY∈Rn×|Y|
∑`∈Y
∑(u,v)∈E
Auv (Yu` − Yv`)2 = arg min
Y∈Rn×|Y|
∑`∈Y
Y`T
∆Y`
s.t. Yu` = Yu`,∀` ∈ Y, ∀ labeled u
Y (t+1)v` ←
∑(u,v)∈E Auv Y (t)
u`
Dvv
Y (t+1) ← D−1AY (t)
Harmonic Property: node = average of neighbors
Aydın Gerek Graph Based Semi-supervised Learning
![Page 20: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/20.jpg)
Gaussian Random Fields (GRF) (Zhu et al., 2003)
also known as Label Propagation
arg minY∈Rn×|Y|
∑`∈Y
∑(u,v)∈E
Auv (Yu` − Yv`)2 = arg min
Y∈Rn×|Y|
∑`∈Y
Y`T
∆Y`
s.t. Yu` = Yu`,∀` ∈ Y, ∀ labeled u
Y (t+1)v` ←
∑(u,v)∈E Auv Y (t)
u`
Dvv
Y (t+1) ← D−1AY (t)
Harmonic Property: node = average of neighbors
Aydın Gerek Graph Based Semi-supervised Learning
![Page 21: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/21.jpg)
Manifold Regularization (Belkin et al., 2006)
Manifold Hypothesis: The data lives in a low dimensionalmanifold embedded in high-dimensional ambient space.
f ∗(x) = arg minf∈HK
1nl
nl∑i=1
L(xi , yi , f ) + λA‖f‖2K + λI‖f‖2I
‖f‖2I =
∫x∈M‖∇Mf‖2dP(x) ≈ 1
nl + nufT ∆f
fTi = f (xi)
Aydın Gerek Graph Based Semi-supervised Learning
![Page 22: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/22.jpg)
Manifold Regularization (Belkin et al., 2006)
Manifold Hypothesis: The data lives in a low dimensionalmanifold embedded in high-dimensional ambient space.
f ∗(x) = arg minf∈HK
1nl
nl∑i=1
L(xi , yi , f )
+ λA‖f‖2K + λI‖f‖2I
‖f‖2I =
∫x∈M‖∇Mf‖2dP(x) ≈ 1
nl + nufT ∆f
fTi = f (xi)
Aydın Gerek Graph Based Semi-supervised Learning
![Page 23: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/23.jpg)
Manifold Regularization (Belkin et al., 2006)
Manifold Hypothesis: The data lives in a low dimensionalmanifold embedded in high-dimensional ambient space.
f ∗(x) = arg minf∈HK
1nl
nl∑i=1
L(xi , yi , f ) + λA‖f‖2K
+ λI‖f‖2I
‖f‖2I =
∫x∈M‖∇Mf‖2dP(x) ≈ 1
nl + nufT ∆f
fTi = f (xi)
Aydın Gerek Graph Based Semi-supervised Learning
![Page 24: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/24.jpg)
Manifold Regularization (Belkin et al., 2006)
Manifold Hypothesis: The data lives in a low dimensionalmanifold embedded in high-dimensional ambient space.
f ∗(x) = arg minf∈HK
1nl
nl∑i=1
L(xi , yi , f ) + λA‖f‖2K + λI‖f‖2I
‖f‖2I =
∫x∈M‖∇Mf‖2dP(x) ≈ 1
nl + nufT ∆f
fTi = f (xi)
Aydın Gerek Graph Based Semi-supervised Learning
![Page 25: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/25.jpg)
Manifold Regularization (Belkin et al., 2006)
Manifold Hypothesis: The data lives in a low dimensionalmanifold embedded in high-dimensional ambient space.
f ∗(x) = arg minf∈HK
1nl
nl∑i=1
L(xi , yi , f ) + λA‖f‖2K + λI‖f‖2I
‖f‖2I =
∫x∈M‖∇Mf‖2dP(x)
≈ 1nl + nu
fT ∆f
fTi = f (xi)
Aydın Gerek Graph Based Semi-supervised Learning
![Page 26: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/26.jpg)
Manifold Regularization (Belkin et al., 2006)
Manifold Hypothesis: The data lives in a low dimensionalmanifold embedded in high-dimensional ambient space.
f ∗(x) = arg minf∈HK
1nl
nl∑i=1
L(xi , yi , f ) + λA‖f‖2K + λI‖f‖2I
‖f‖2I =
∫x∈M‖∇Mf‖2dP(x) ≈ 1
nl + nufT ∆f
fTi = f (xi)
Aydın Gerek Graph Based Semi-supervised Learning
![Page 27: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/27.jpg)
Manifold Regularization (Belkin et al., 2006)
Manifold Hypothesis: The data lives in a low dimensionalmanifold embedded in high-dimensional ambient space.
f ∗(x) = arg minf∈HK
1nl
nl∑i=1
L(xi , yi , f ) + λA‖f‖2K + λI‖f‖2I
‖f‖2I =
∫x∈M‖∇Mf‖2dP(x) ≈ 1
nl + nufT ∆f
fTi = f (xi)
Aydın Gerek Graph Based Semi-supervised Learning
![Page 28: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/28.jpg)
Manifold Regularization (Belkin et al., 2006)
Manifold Hypothesis: The data lives in a low dimensionalmanifold embedded in high-dimensional ambient space.
f ∗(x) = arg minf∈HK
1nl
nl∑i=1
L(xi , yi , f ) + λA‖f‖2K + λI‖f‖2I
‖f‖2I =
∫x∈M‖∇Mf‖2dP(x) ≈ 1
nl + nufT Lf
fTi = f (xi)
Aydın Gerek Graph Based Semi-supervised Learning
![Page 29: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/29.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di
, Z ∈ Rn×do
H(l) ∈ Rn×dl , H(0) = X ,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning
![Page 30: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/30.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di , Z ∈ Rn×do
H(l) ∈ Rn×dl , H(0) = X ,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning
![Page 31: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/31.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di , Z ∈ Rn×do
H(l) ∈ Rn×dl
, H(0) = X ,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning
![Page 32: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/32.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di , Z ∈ Rn×do
H(l) ∈ Rn×dl , H(0) = X
,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning
![Page 33: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/33.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di , Z ∈ Rn×do
H(l) ∈ Rn×dl , H(0) = X ,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning
![Page 34: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/34.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di , Z ∈ Rn×do
H(l) ∈ Rn×dl , H(0) = X ,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning
![Page 35: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/35.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di , Z ∈ Rn×do
H(l) ∈ Rn×dl , H(0) = X ,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning
![Page 36: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/36.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di , Z ∈ Rn×do
H(l) ∈ Rn×dl , H(0) = X ,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I
, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning
![Page 37: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/37.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di , Z ∈ Rn×do
H(l) ∈ Rn×dl , H(0) = X ,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning
![Page 38: Graph Based Semi-supervised Learning - GitHub PagesGraph Based Semi-supervised Learning Aydın Gerek Marmara University May 26th, 2018 Aydın Gerek Graph Based Semi-supervised Learning](https://reader034.fdocuments.in/reader034/viewer/2022050715/5f0f4e377e708231d44380f3/html5/thumbnails/38.jpg)
Graph Convolutional Networks (Kipf and Welling 2017)
X ∈ Rn×di , Z ∈ Rn×do
H(l) ∈ Rn×dl , H(0) = X ,H(L) = Z
H(l+1) = f (H(l),A)
f (H(l),A) = σ(AH(l)W (l))
A = A + I, D−1/2AD−1/2
f (H(l),A) = σ(D−1/2AD−1/2H(l)W (l))
Aydın Gerek Graph Based Semi-supervised Learning