using evolutionary computing for feature-driven graph generation
TRANSCRIPT
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Using Evolutionary Computing for Feature-
driven Graph GenerationMerijn Verstraaten, Ana Lucia Varbanescu &
Cees de Laat
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Performance Quiz
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Structural Properties#V #E ACC Triangles Diameter
90% Diameter
as-Skitter 1.696.415 11.095.298 0,2581 28.769.868 25 6
cit-Patents 3.774.768 16.518.948 0,0757 7.515.023 22 9,4
email-EuAll 265.214 420.045 0,0671 267.313 14 4,5
Facebook 4.039 88.234 0,6055 1.612.010 8 4,7
GPlus 107.614 13.673.453 0,4901 1.073.677.742 6 3
roadNet-CA 1.965.206 2.766.607 0,0464 120.676 849 500
roadNet-TX 1.379.917 1.921.660 0,047 82.869 1.054 670
soc-Livejournal 4.847.571 68.993.773 0,2742 285.730.264 16 6,5
Twitter 81.306 1.768.149 0,5653 13.082.506 7 4,5
web-BerkStan 685.230 7.600.595 0,5967 64.690.980 514 9,9
web-Google 875.713 5.105.039 0,5143 13.391.903 21 8,1
wikiTalk 2.394.385 5.021.410 0,0526 9.203.519 9 4
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Structural PropertiesNumber of vertices
Number of edges
Edge properties
Vertex properties
Directivity
Connectivity
Centrality – betweenness, degree, edge, PageRank(?)
Chromatic number
Cycles
Assortativity
Treewidth
Average degree
Average distance
Diameter
Max degree
Degree distribution
Clustering Coefficient
Number of triangles
Max-clique
Modularity
Eigenvalue and second eigenvalue
Degeneracy
Motif profile
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Generator Wishlist
Set of relevant properties
Independently variable (if possible)
Easy to extend set
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Start
Generate intial population
Determine fitness
Acceptable solution found
Select parents Crossover
Mutation
Select survivors
End Yes
No
Evolutionary Computing
Good at:
Large search space
Complex, interdependent parameters
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Representations
Connectivity matrices
Edge lists
Generating functions
Generators
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0
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Connectivity Matrix
0 1 2 3 4 5
0 0 1 0 0 1 0
1 0 0 1 0 1 0
2 0 0 0 1 0 0
3 0 0 0 0 1 0
4 0 0 0 0 0 0
5 0 0 0 1 0 0
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Pros & Cons
Pros:
Easy to implement primitives
Fixed number of vertices
Cons:
Number of edges not fixed
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Exponential Degree
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Gaussian Degree
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Uniform Degree
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Results
+ Substantially faster than Bach, et al. & Bailey, et al.
- Graphs >1.000 vertices converge too slowly
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Future WorkExperiment with different primitives
Evaluate the HyperNEAT approach
Miscellaneous ObservationsPrimitives matter (edgewise vs vertexwise)
Need better mutation
Minimum necessary size?
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Questions? Suggestions? Comments?
... are welcome live or online!
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Existing Generators
Complex Networks: Erdös-Rényi R-MAT Kronecker graphs
Misc: Social networks Freescale Power law etc.
Problems: Focus on social graphs Limited expressivity Not easily extensible
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NeuroEvolution of Augmenting Topologies
(NEAT)Pros:
Very expressive Good results
Cons: Scalability Slow…
HyperNEAT: Generate generating functions
Pros: ``Webscale’’
Cons: Unclear impact on expressivity
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More…Bach, et al.
Interactive random graph generation with evolutionary algorithms
Bailey, et al.
Automatic generation of graph models for complex networks by genetic programming.