Attributed Graphs Yu Su University of California at Santa Barbara with Fangqiu Han Richard E Harang and Xifeng Yan Introduction A Fast Kernel for Attributed Graphs Graph Kernel ID: 526899
Download Presentation The PPT/PDF document "A Fast Kernel for" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
A Fast Kernel for Attributed Graphs
Yu SuUniversity of California at Santa Barbarawith Fangqiu Han, Richard E. Harang, and Xifeng Yan Slide2
IntroductionA Fast Kernel for Attributed GraphsSlide3
Graph KernelA graph kernel defines a similarity measure
over graphs — a core problem in graph miningInner product in some (latent) feature space Decouple data representation from learning machineOnce a graph kernel is supplied, a whole toolbox of kernel machines become readily applicableSVM, Kernel PCA, Support Vector Regression, Clustering, etc.
A good graph kernel is thus the key
A Fast Kernel for Attributed GraphsSlide4
Chemo- & Bioinformatics
Semantic web
Software Engineering
Natural Language Processing
Broad Applications
A Fast Kernel for Attributed GraphsSlide5
Trends and Challenges in the Big Data Era
A Fast Kernel for Attributed GraphsIncreasing graph size
More efficient
methodsMore versatile methods
Richer graph attributes
This work: A
linear-time
kernel that can handle
both categorical and numerical attributes.Slide6
Graph Kernel as a Measure of Graph SimilarityDecompose each graph into a (multi-)set of features
Subgraphs (Gartner et al. 2003, NP-hard!)Random walks (Gartner et al. 2003, Kashima et al. 2003) Subtrees
(Shervashidze and Borgwardt 2009)Vectors (Neumann et al. 2016)
A Fast Kernel for Attributed GraphsSlide7
Graph Kernel as a Measure of Graph SimilarityDecompose each graph into a (multi-)set of features
Subgraphs (Gartner et al. 2003, NP-hard!)Random walks (Gartner et al. 2003, Kashima et al. 2003) Subtrees
(Shervashidze and Borgwardt 2009)Vectors (Neumann et al. 2016)
A Fast Kernel for Attributed GraphsSlide8
Graph Kernel as a Measure of Graph SimilarityDecompose each graph into a (multi-)set of features
Subgraphs (Gartner et al. 2003, NP-hard!)Random walks (Gartner et al. 2003, Kashima et al. 2003) Subtrees
(Shervashidze and Borgwardt 2009)Vectors (Neumann et al. 2016)
Compare feature setsPair-wise comparison (quadratic)
A Fast Kernel for Attributed GraphsSlide9
Graph Kernel as a Measure of Graph SimilarityDecompose each graph into a (multi-)set of features
Subgraphs (Gartner et al. 2003, NP-hard!)Random walks (Gartner et al. 2003, Kashima et al. 2003) Subtrees
(Shervashidze and Borgwardt 2009)Vectors (Neumann et al. 2016)
Compare feature setsPair-wise comparison (quadratic)Inner product (
linear
;
only when features are discrete
)
A Fast Kernel for Attributed GraphsSlide10
Graph Kernel as a Measure of Graph SimilarityDecompose each graph into a (multi-)set of features
Subgraphs (Gartner et al. 2003, NP-hard!)Random walks (Gartner et al. 2003, Kashima et al. 2003) Subtrees
(Shervashidze and Borgwardt 2009)Vectors (Neumann et al. 2016)
Compare feature setsPair-wise comparison (quadratic)Inner product (
linear
;
only when features are discrete
)
Discretization (
linear
;
can handle numerical attributes
)
A Fast Kernel for Attributed GraphsSlide11
Graph Kernel as a Measure of Graph SimilarityDecompose each graph into a (multi-)set of features
Subgraphs (Gartner et al. 2003, NP-hard!)Random walks (Gartner et al. 2003, Kashima et al. 2003) Subtrees
(Shervashidze and Borgwardt 2009)Vectors (Neumann et al. 2016)
Compare feature setsPair-wise comparison (quadratic)Inner product (
linear
;
only when features are discrete
)
Discretization
(
linear
;
can handle numerical attributes
)
A Fast Kernel for Attributed Graphs
vector features + discretizationSlide12
MethodA Fast Kernel for Attributed GraphsSlide13
Descriptor Matching (DM) Kernel: An OverviewA Fast Kernel for Attributed GraphsSlide14
Descriptor Matching (DM) Kernel: An OverviewA Fast Kernel for Attributed GraphsSlide15
Descriptor Matching (DM) Kernel: An OverviewA Fast Kernel for Attributed GraphsSlide16
Desired Descriptor Property: Preserve Similarity Similar nodes should have similar descriptorsSo it
becomes meaningful to compare graph similarity by matching their descriptorsNodes are more similar if their attributes and neighbors are more similarRecursive definition of similarity makes it natural to generate descriptors in a
recursive mannerA Fast Kernel for Attributed GraphsSlide17
Desired Descriptor Property: Highly DiscriminativeA Fast Kernel for Attributed GraphsSlide18
Descriptor Generation via PropagationA Fast Kernel for Attributed GraphsSlide19
Descriptor MatchingOptimal matching: Maximum weighted bipartite matching
Cubic time. Not a valid kernel (Vert 2008)
A Fast Kernel for Attributed GraphsSlide20
Descriptor MatchingOptimal matching: Maximum weighted bipartite matching
Cubic time. Not a valid kernel (Vert 2008)Discretization: Uniform binningLinear time.
Valid kernel. Unweighted, independent bins.
A Fast Kernel for Attributed GraphsSlide21
Descriptor MatchingOptimal matching: Maximum weighted bipartite matching
Cubic time. Not a valid kernel (Vert 2008)Discretization: Uniform binningLinear time.
Valid kernel. Unweighted, independent bins.Discretization: Data-dependent hierarchical binningLinear time. Valid kernel. Weighted, multi-resolution bins.
Vocabulary-Guided pyramid matching (VG) kernel (Grauman and Darrell 2006)
A Fast Kernel for Attributed GraphsSlide22
Descriptor MatchingOptimal matching: Maximum weighted bipartite matching
Cubic time. Not a valid kernel (Vert 2008)Discretization: Uniform binningLinear time.
Valid kernel. Unweighted, independent bins.Discretization: Data-dependent hierarchical binningLinear time. Valid
kernel. Weighted, multi-resolution bins.Vocabulary-Guided pyramid matching (VG) kernel (Grauman and Darrell 2006)
A Fast Kernel for Attributed GraphsSlide23
Descriptor Matching via Pyramid Matching Kernel
A Fast Kernel for Attributed GraphsSlide24
Descriptor Matching via Pyramid Matching Kernel
A Fast Kernel for Attributed GraphsSlide25
Descriptor Matching via Pyramid Matching Kernel
A Fast Kernel for Attributed GraphsSlide26
Descriptor Matching via Pyramid Matching KernelA Fast Kernel for Attributed GraphsSlide27
Descriptor Matching via Pyramid Matching KernelA Fast Kernel for Attributed GraphsSlide28
Descriptor Matching via Pyramid Matching KernelA Fast Kernel for Attributed GraphsSlide29
Descriptor Matching via Pyramid Matching KernelA Fast Kernel for Attributed GraphsSlide30
Descriptor Matching via Pyramid Matching KernelA Fast Kernel for Attributed GraphsSlide31
EvaluationA Fast Kernel for Attributed GraphsSlide32
Efficiency on Synthetic GraphsA Fast Kernel for Attributed Graphs
Number of nodes
DM:
this workPK: ML’16GH:
NIPS’13
WLSP:
JMLR’11
SP:
ICDM’05
CSM:
ICML’12Slide33
Accuracy on Real-world GraphsA Fast Kernel for Attributed Graphs
DM is among the best in 9 out of the 10 datasets, and is significantly better than PK on 8
dataset (Student’s t test at p=0.05). Slide34
SummariesA graph kernelCan be computed in linear time
w.r.t. graph sizeCan handle both categorical and numerical attributesKey ideasDescriptor generation via categorical attribute propagation
Descriptor matching via hierarchical data-dependent discretizationCompetitive performanceEfficient: scale to graphs with 100,000 nodesAccurate: best on 9 out of 10 datasets
A Fast Kernel for Attributed GraphsSlide35
A Fast Kernel for Attributed Graphs
Thank You!