Genetic Approximate Matching of Attributed Relational Graphs

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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
1
1
2
4
2
3
4
3
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GA - Crossover
1
1
4
2
4
2
3
3

• 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

1 3 4 2 5
4 1 2 3 5
1 2 3 4 5
1 4 2 3 5
2 3 4 1 5
3 1 5 2 4
2 1 5 4 3
4 2 5 3 1
X x x
4 1 3 5
1 3 2 5
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GA Local Search

• Neighborhood N

• Fitness evaluation of the neighborhood

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GA other parameters
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Combining GA with A




GA
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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

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Thanks for your attention