1. Inexact Matching of ontology graphs using expectation maximization
Universidad Autónoma de Madrid -15 Enero 2010
Inexact Matching of ontology graphs using expectation maximization
Prashant Doshi, Ravikanth Kolli, Christopher Thomas
Web Semantics: Science, Services and Agents on the World Wide Web 2009
Keywords: ontology, matching, expectation-maximization

2. Agenda Introduction Expectation Maximization Ontology Schema Model
Universidad Autónoma de Madrid -15 Enero 2010
Agenda
Introduction
Expectation Maximization
Ontology Schema Model
Graph Matching with GEM
Random sampling and Heuristics
Computational complexity
Initial Results
Large ontologies
Benchmarks
Conclusions

3. Universidad Autónoma de Madrid -15 Enero 2010
Introduction
Growing usefulness of semantic web based on the increasingly number of ontologies
OWL and RDF are labeled-directed-graph ontology representation languages
Formulation ‘Find the most likely map between the two ontologies’*

4. Expectation Maximization
Universidad Autónoma de Madrid -15 Enero 2010
Expectation Maximization
Technique to find the maximum likelihood estimate of the underlying model from observed data in the presence of missing data.
E-Step
Formulation of the estimate
M-Step
Search for the maximum of the estimate
Relaxed search using: GEM

5. Ontology Schema Model OWL y RDF (labeled directed graphs)
Universidad Autónoma de Madrid -15 Enero 2010
Ontology Schema Model
OWL y RDF (labeled directed graphs)
Labels are removed, constructing a bipartite graph.

6. Graph matching GEM Maximum likelyhood estimate problem
Universidad Autónoma de Madrid -15 Enero 2010
Graph matching GEM
Maximum likelyhood estimate problem
Hidden variables: mapping matrix
Local search guided by GEM
Search-Space

7. Universidad Autónoma de Madrid -15 Enero 2010
Graph matching GEM
M* gives the maximum conditional probability of the data graph Od given Om.
Only many-one matching
Focused on homeomorphisms

8. Graph matching GEM
MLE problem with respect to map hidden variables

9. Graph matching GEM
Need to maximize:

10. Graph matching GEM
Probability that xa is in correspondence with ya given the assignment model
Each of the hidden variables

11. Graph matching GEM
Graph constraints
And Smith-Waterman

12. Graph matching GEM Exhaustive search not possible
Universidad Autónoma de Madrid -15 Enero 2010
Graph matching GEM
Exhaustive search not possible
Problem: local maxima
Use K random models + heuristics
If two classes are mapped, map their parents + Random restart

13. Computational complexity
Universidad Autónoma de Madrid -15 Enero 2010
Computational complexity
SW technique is O(L2)
EM mapping is O(K*(|Vm|*|Vd|)2 )

14. Universidad Autónoma de Madrid -15 Enero 2010
Initial Experiments

15. Universidad Autónoma de Madrid -15 Enero 2010
Large Ontologies

16. Universidad Autónoma de Madrid -15 Enero 2010
Benchmarks

17. Conclusions Structure and Syntactic vs External Resources
Universidad Autónoma de Madrid -15 Enero 2010
Conclusions
Structure and Syntactic vs External Resources
Weak performance: dissimilar names and structure
Good performance: extensions and flattening
Not scalable : partitioning and extension
No longer GEM, but converges
Future work: Markov Chain MonteCarlo methods
Extensible algorithm: can include other aproaches