Inexact Matching of ontology graphs using expectation maximization

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Presentation transcript:

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

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

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’*

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

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.

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

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

Graph matching GEM MLE problem with respect to map hidden variables

Graph matching GEM Need to maximize:

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

Graph matching GEM Graph constraints And Smith-Waterman

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

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

Universidad Autónoma de Madrid -15 Enero 2010 Initial Experiments

Universidad Autónoma de Madrid -15 Enero 2010 Large Ontologies

Universidad Autónoma de Madrid -15 Enero 2010 Benchmarks

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