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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 Universidad Autónoma de Madrid -15 Enero 2010

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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

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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’* Universidad Autónoma de Madrid -15 Enero 2010

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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 Universidad Autónoma de Madrid -15 Enero 2010

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

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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

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

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Graph matching GEM MLE problem with respect to map hidden variables

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Graph matching GEM Need to maximize:

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Graph matching GEM Probability that x a is in correspondence with y a given the assignment model Each of the hidden variables

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Graph matching GEM Graph constraints And Smith-Waterman

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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 Universidad Autónoma de Madrid -15 Enero 2010

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Computational complexity SW technique is O(L 2 ) EM mapping is O(K*(|V m |*|V d |) 2 ) Universidad Autónoma de Madrid -15 Enero 2010

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Initial Experiments Universidad Autónoma de Madrid -15 Enero 2010

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Large Ontologies Universidad Autónoma de Madrid -15 Enero 2010

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Benchmarks Universidad Autónoma de Madrid -15 Enero 2010

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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 Universidad Autónoma de Madrid -15 Enero 2010

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