Genetic Approximate Matching of Attributed Relational Graphs Thomas Bärecke¹, Marcin Detyniecki¹,...

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

T. Bärecke et al. Genetic Approximate Matching of ARGs

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Motivation 1/2

•Frontal•Neutral expression

T. Bärecke et al. Genetic Approximate Matching of ARGs

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Motivation 2/2

T. Bärecke et al. Genetic Approximate Matching of ARGs

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Outline

EC Subgraph Isomorphism Genetic Approach

Encoding Crossover Local search Combination with tree search

Results Conclusions and Future Work

T. Bärecke et al. Genetic Approximate Matching of ARGs

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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

T. Bärecke et al. Genetic Approximate Matching of ARGs

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GA - Encoding

1

3

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2

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nS

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T. Bärecke et al. Genetic Approximate Matching of ARGs

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GA - Crossover

Fitness change depends on all other elementary mappings

Strict position-based crossover (PBX)

1

3

42

1

3

42

T. Bärecke et al. Genetic Approximate Matching of ARGs

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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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T. Bärecke et al. Genetic Approximate Matching of ARGs

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GA – Local Search

Neighborhood N

MN '

Fitness evaluation of the neighborhood

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T. Bärecke et al. Genetic Approximate Matching of ARGs

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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

T. Bärecke et al. Genetic Approximate Matching of ARGs

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Combining GA with A*

…

…

GA

…

…

T. Bärecke et al. Genetic Approximate Matching of ARGs

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Outline

EC Subgraph Isomorphism Genetic Approach Results

Evolution Precision Run time Combined method

Conclusions and Future Work

T. Bärecke et al. Genetic Approximate Matching of ARGs

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Evolution Process

False Mappings Fitness

T. Bärecke et al. Genetic Approximate Matching of ARGs

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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

T. Bärecke et al. Genetic Approximate Matching of ARGs

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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