genetic approximate matching of attributed relational graphs thomas bärecke¹, marcin detyniecki¹,...
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Genetic Approximate Matching of Attributed Relational Graphs
Thomas Bärecke¹, Marcin Detyniecki¹, Stefano Berretti² and Alberto Del Bimbo²
¹ Université Pierre et Marie Curie - Paris6 UMR 7606, DAPA, LIP6, Paris, France
² Università degli Studi di Firenze, Dipartimento di Sistemi e Informatica, Florence, Italy
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Motivation 1/2
•Frontal•Neutral expression
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Motivation 2/2
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Outline
EC Subgraph Isomorphism Genetic Approach
Encoding Crossover Local search Combination with tree search
Results Conclusions and Future Work
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EC (Sub-)Graph Isomorphism
No known optimal and efficient algorithm
Genetic algorithms “Parallel” exploration of
large non-continuous search spaces
No perfect exploitation Adaptive stop criterion
Solution quality Elapsed time
Good solutions in reasonable time
Optimal algorithms Exponential complexity Max. 15 vertices
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GA - Encoding
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nS
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GA - Crossover
Fitness change depends on all other elementary mappings
Strict position-based crossover (PBX)
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Strict position-based crossover Create position list and shuffle it Uniformly select crossover points Create children
In case of collision place in alternative place Fill in missing values
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GA – Local Search
Neighborhood N
MN '
Fitness evaluation of the neighborhood
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GA – other parameters
Name Value
Tournament size 2
Termination 10
Crossover probability 0.9
Mutation probability 0
2-opt probability 1
Population size 100
UPMX ratio 0.33
Elitism 1
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Combining GA with A*
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GA
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…
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Outline
EC Subgraph Isomorphism Genetic Approach Results
Evolution Precision Run time Combined method
Conclusions and Future Work
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Evolution Process
False Mappings Fitness
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Diversity
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Precision – Crossover 1/2
PBX PMX
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Precision – Crossover 2/2
PBX UPMX
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Results - Runtime
Graph size Noise (Size 50)
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Combined results
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Conclusions
Permutation based Genetic Algorithm Robust for Subgraph Matching Crossover operator Local search Solution candidate at any time
Combination of exact and approximate methods
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Future Work
Real world data! Allow more graph edit operations Better local improvement heuristic Fewer and optimal parameters Comparison with cycle crossover
Thanks for your attention