nips2016 mlgkernel
TRANSCRIPT
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
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NIPS 2016
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�(x)
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�(x)
�(x)
k(xi, xj) = ��(xi), �(xj)�
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k(xi, xj)
�(x)?
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�(x)
k(xi, xj)
�(x)
k
k(xi, xj) = ��(xi), �(xj)�
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k(xi, xj)
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The Multiscale Laplacian Graph Kernel Risi Kondor : University of Chicago Horace Pan : University of Chicago
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global structure
local structure
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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�1UTUL�1UT
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LGLG
LG
kLG
kFLG
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LGLG
LG
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LG
LG l Gl
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LG
LG
} LG
l Gl
kFLG(Gl, G�l)
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LG
LG
} kFLG(Gl, G�l)
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LG
LG
} Kl(v, v�)
kFLG(Gl(v), Gl(v�))
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LG
→
} Kl(v, v�)
Kl(v, v�) l
kFLG(Gl(v), Gl(v�))
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LG
}Kl(v, v�)
l + 1
kFLG(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�)
kFLG(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
kKlFLG(Gl+1(v), Gl+1(v
�))
Kll
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LG
ll = 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
ll = 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�) = kKl�1
FLG(Gl(v), Gl(v�))
l
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LG
Multiscale Laplacian Graph Kernel
ll = 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) = kKLFLG(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