Quelle IA pour les données structurées ?
Graph Kernels
Romain Raveaux
[email protected] Maître de conférences
Université de Tours
Laboratoire d’informatique (LIFAT) Equipe RFAI
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Outline
• Graph kernel
• Definition
• Kernel trick
• Examples of graph kernels:
• Simple
• Random walk kernels
• Application
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Previous episode
• Graph Neural Networks
• http://romain.raveaux.free.fr/document/graph%20neural%20networks%20ro main%20raveaux.pdf
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Graph kernel
Taxonomy:
Graph embedding
Explicit embedding Implicit embedding
Graph kernel Graph space
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A kernel
Kernel Trick
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Kernel Trick
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Kernel Trick
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Kernel Trick
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Graph kernel : theoretical issues
• To design a kernel taking the whole graph structure into account
amounts to build a complete graph kernel that distinguishes between 2 graphs only if they are not isomorphic
• Complete graph kernel design is theoretically possible … but practically infeasible (NP-hard)
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Graph Kernel Families
• Diffusion kernels (from similarity matrix)
• Convolution kernel
• Walk kernel (from adjacency matrix)
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Graph embedding
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𝑘𝑥 𝐺, 𝐺′ =
𝑖,𝑗=1
|𝑉𝑥|
[
𝑘=0
∞
𝜆𝑘𝐴𝑘𝑥]
𝑖𝑗
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Some experiments
• Comparison between graph kernels and graph neural networks.
• Taken from :
• How Powerful are Graph Neural Networks? (2018)
• Keyulu Xu, Weihua Hu, Jure Leskovec, Stefanie Jegelka
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Summary on graph kernels
• Comparing paths of two different graphs is polynomial
• Comparing subgraphs of two different graphs optimally is not guaranteed in polynomial time.
• Kernels that take into account numeric attributes are more challenging.
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