Read and introduce 'The Multiscale Laplacian Graph Kernel (NIPS 2016 paper)' at Waseda University.

1. The Multiscale Laplacian
Graph Kernel
Risi Kondor
Department of Computer Science and
Department of Statistics,
University of Chicago
Horace Pan
Department of Computer Science,
University of Chicago
B4
1
NIPS 2016

2. 2

3. 3
(x)

4. 4
(x)
(x)
k(xi, xj) = (xi), (xj)

5. 5
k(xi, xj)
(x)?

6. 6
(x)
k(xi, xj)
(x)
k
k(xi, xj) = (xi), (xj)

7. 7

8. 8
k(xi, xj)

9. 9
The Multiscale Laplacian Graph Kernel
Risi Kondor : University of Chicago
Horace Pan : University of Chicago

10. 10

11. 11
global structure local structure

12. 12

13. 13
Multiscale Laplacian Graph Kernel MLG

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graph Laplacian LG

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LG
LG
wi,j

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LG

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LG

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LG

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LG
vj (vj)
U = [ (v1), (v2), . . . , (vn)]
UL 1
UT
UL 1
UT

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LG
LG
LG
kLG
kF LG

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LG
LG
LG

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LG
LG
l Gl

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LG
LG
}
LG
l Gl
kF LG(Gl, Gl)

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LG
LG
}kF LG(Gl, Gl)

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LG
LG
} Kl(v, v )
kF LG(Gl(v), Gl(v ))

26. 26
LG
→
} Kl(v, v )
Kl(v, v ) l
kF LG(Gl(v), Gl(v ))

27. 27
LG
}
Kl(v, v )
l + 1
kF LG(Gl+1(v), Gl+1(v ))
l

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LG
}
Kl(v, v )
l + 1 Kl+1(v, v )
Kl+1(v, v )
kF LG(Gl+1(v), Gl+1(v ))
l

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LG
}
Kl(v, v )
l + 1 Kl+1(v, v )
Kl+1(v, v )
l
kKl
F LG(Gl+1(v), Gl+1(v ))
Kll

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LG
l
l = 0, 1, 2, . . . , L
l = 0, 1, 2, . . . , Ll = 0, 1, 2, . . . , Ll = 0, 1, 2, . . . , L l = 0, 1, 2, . . . , L

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LG
l
l = 0, 1, 2, . . . , L
l = 0, 1, 2, . . . , Ll = 0, 1, 2, . . . , Ll = 0, 1, 2, . . . , L l = 0, 1, 2, . . . , L
Kl(v, v ) = k
Kl 1
F LG(Gl(v), Gl(v ))
l

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LG
Multiscale Laplacian Graph Kernel
l
l = 0, 1, 2, . . . , L
l = 0, 1, 2, . . . , Ll = 0, 1, 2, . . . , Ll = 0, 1, 2, . . . , L l = 0, 1, 2, . . . , L
K(G1, G2) = kKL
F LG(G1, G2)

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ENZYMES dataset
600 32
16 2

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SVM

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SVM
some of top performance graph kernels
Weisfeiler-Lehman Kernel
Weisfeiler-Lehman Edge Kernel
Shortest Path Kernel
Graphlet Kernel
p-random Walk Kernel

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NCI1, NCI109
Weisfeiler Lehman / Weisfeiler Lehman Edge Kernel

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LG FLG kernel
LG MLG kernel

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multiresolution structure

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Appendix

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(x)
(xi), (xj) = k(xi, xj)
k(xi, xj)
(x)

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LG