inexact matching of ontology graphs using expectation maximization prashant doshi, ravikanth kolli,...

Inexact Matching of ontology graphs using expectation

maximizationPrashant 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

Agenda

Introduction Expectation Maximization Ontology Schema Model Graph Matching with GEM

• Random sampling and Heuristics• Computational complexity• Initial Results

Large ontologies Benchmarks Conclusions


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

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) Labels are removed, constructing a bipartite

graph.


Graph matching GEM

Maximum likelyhood estimate problem• Hidden variables: mapping matrix

Local search guided by GEM• Search-Space


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 Problem: local maxima Use K random models + heuristics

• If two classes are mapped, map their parents + Random restart


Computational complexity

SW technique is O(L2)

EM mapping is O(K*(|Vm|*|Vd|)2 )


Initial Experiments


Large Ontologies


Benchmarks


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


inexact matching of ontology graphs using expectation maximization prashant doshi, ravikanth kolli,...

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