A posteriori evaluation of Ontology Mapping results Graph-based methods for Ontology Matching

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A posteriori evaluation of Ontology Mapping results Graph-based methods for Ontology Matching. Ondej vb KIZI. Agenda. Conference track within OAEI-2006 Initial manual empirical evaluation Empirical Evaluation via Logical Reasoning Mapping debugging based on Drago system - PowerPoint PPT Presentation

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<ul><li><p>*for KEG seminar*A posteriori evaluation of Ontology Mapping results</p><p> Graph-based methodsfor Ontology MatchingOndej vbKIZI</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*AgendaConference track within OAEI-2006Initial manual empirical evaluationEmpirical Evaluation via Logical ReasoningMapping debugging based on Drago systemExperiments with OntoFarm collectionConsensus Building WorkshopMining over the mappings with meta-data</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*AgendaConference track within OAEI-2006Initial manual empirical evaluationEmpirical Evaluation via Logical ReasoningMapping debugging based on Drago systemExperiments with OntoFarm collectionConsensus Building WorkshopMining over the mappings with meta-data</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Conference track - FeaturesBroadly understandable domain Conference organisationFree exploration by participants within 10 ontologiesNo a priori reference alignmentParticipants: 6 research groups</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Conference track - Datasethttp://nb.vse.cz/~svabo/oaei2006/index2.htmlOntoFarm collection</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Conference track - Participants6 participantsAutomsComa++OWL-CtxMatchFalconHMatchRiMOM</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Conference track - GoalsFocus on interesting mappings and unclear mappingsWhy should they be mapped?Arguments: against and forWhich systems did discover them?Differences in similarity measuresUnderlying techniques?</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*EvaluationProcessing all mappings by handAssessment based on personal judgement of organisers (consistency problem)Tags: TP, FP, interesting, ?, heterogenous mapping Types of errors and phenomena: subsumption, inverse property, siblings, lexical confusion </p><p>for KEG seminar</p></li><li><p>*for KEG seminar*EvaluationSubsumption mistaken for equivalenceAuthor,Paper_AuthorConference_Trip, Conference_partInverse propertyhas_author,authorOfSiblings mistaken for equivalenceProgramCommittee,Technical_commiteeLexical confusion errorprogram,Program_chairRelation Class mappinghas_abstract,AbstractTopic,coversTopic; read_paper,Paper</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*EvaluationSome statistics as a side-effect of processing</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Evaluation</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*AgendaConference track within OAEI-2006Initial manual empirical evaluationEmpirical Evaluation via Logical ReasoningMapping debugging based on Drago systemExperiments with OntoFarm collectionConsensus Building WorkshopMining over the mappings with meta-data</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mapping debuggingGoal: to improve the quality of automatically generated mapping sets using logical reasoning about mappingsPrototype of the debugger/minimezer implemented on top of the DRAGO DDL reasonerSemi-automatic process</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Drago Distributed Reasoning Architecture for Galaxy of OntologiesTool for distributed reasoningBased on DDL (Distributed Description Logics)Servicescheck ontology consistency,build classification,verify concepts satisfiability, check entailment</p><p>Resource: [http://drago.itc.it/]</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*DDLRepresentation framework for semantically connected ontologiesExtension of Description Logics (local interpretation, distributed ,)Distributed T-boxSemantic relations represented via directed bridge-rules: bridge rules:</p><p>From the point of view of ontology j</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*DDL inference mechanismExtension of tableau algorithmInference of new subsumption via subsumption propagation mechanism</p><p>And its generalized form with disjunctions,</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Drago - architectureDRP=Drago Reasoning Peerpeer-peer network of DRPs</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Drago - implementationOntological language OWLMapping between ontologies represented in C-OWL</p><p>Distributed Reasoner extension of OWL reasoner Pellet (http://www.mindswap.org/2003/pellet/)</p><p>Communication amongst DRP via HTTP</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mapping debugging1st step: diagnosis - detect unsatisfiable concepts (inconsistent ontology)Assumption: semantically connected ontologies are consistent (without unsatisfiable concepts)Therefore, unsatisfiable concepts in target ontology are caused by some mappings</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mapping debugging2nd step: discovering minimal conflict set Two conditions:Set of mappings causing inconsistency andBy removing a mapping, concept is satisfiable3rd step: debuggingUser feedbackRemoving mapping with the lowest degree of confidenceCompute semantic distance of the concept names using WordNet synsets</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mapping debugging4th step: minimizationRemoving redundant mappingsIt leads to minimal mappings set with all the semantics (logically-equivalent minimal version)</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Experiments with OntoFarmMapping between class namesSix ontologies involved, Results from four matching systems were analysedResults of reasoning-based analysis:</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Experiments with OntoFarmInterpretation: 1. the lower number of inconsistent alignments, the better quality of mappings 2. this analysis reveal non-obvious errors in mappings</p><p>obivously incorrect mappingsnon-obivous errors in mappings</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*AgendaConference track within OAEI-2006Initial manual empirical evaluationEmpirical Evaluation via Logical ReasoningMapping debugging based on Drago systemExperiments with OntoFarm collectionConsensus Building WorkshopMining over the mappings with meta-data</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Consensus Building WorkshopDiscussion about interesting mappings discovered during manual and automatic evaluationReaching agreementWhy should they be mapped?Arguments: against and forDuring discussion the following order of arguments were taken into account:lexical reasonscontext of elements (subclasses superclasses, subproperties, superproperties), consider extensions of classes (set interpretation)Properties related to classesAxioms (more complex restrictions)</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Ilustrative examplesPerson vs. Human</p><p>Against: different sets of subconceptsFor: the same domainResult: YES</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Ilustrative examplesPC_Member vs. Member_PC</p><p>Who is the member of ProgramCommittee?</p><p>Ontologies have different interpretation.</p><p>Either PC_Chair=Chair_PCor PC_Member=Member_PC</p><p>result: PC_Chair=Chair_PCTherefore:PC_Member!=Member_PC</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Ilustrative examplesRejection vs. RejectBoth are related to the outcome of the review of a submitted paperTheir position in taxonomy reveal differences in meaning</p><p>Reccommendation is inputDecision is outputof the process of revieving</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Ilustrative examplesLocation vs. PlaceLocation relates to the country and city where conference is heldPlace relates to parts of building where particular events take place</p><p>It is need to look at the range and domain restrictions of related properties:</p><p>Location is domain of properties: locationOfLocation is range of properties: heldIn</p><p>iasted:Place is domain of properties: is_equipped_bysigkdd:Place is range of properties: can_stay_in</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Lessons learnedRelevance of contextLexical matching not enoughLocal structure not enough?Advice: employ semantics, background knowledge (eg. Recommendation and Decision case)Semantic relationsEquivalent mappings quite often lead to inconsistenciesMany concepts are closely related but not exactly the sameAdvice: discover not only equivalent mappings</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Lessons learnedAlternative Interpretations (intended meaning)incomplete specification in ontologies lead to diverse interpretations (PC_Member case), Advice: check consistency of proposed mappings </p><p>for KEG seminar</p></li><li><p>*for KEG seminar*AgendaConference track within OAEI-2006Initial manual empirical evaluationEmpirical Evaluation via Logical ReasoningMapping debugging based on Drago systemExperiments with OntoFarm collectionConsensus Building WorkshopMining over the mappings with meta-data</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mining over the mappings with meta-dataIntroduction to Mapping PatternsMining4ft-MinerMining over Mapping Results</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mapping patternsDeal with (at least) two ontologiesReflect the structure of ontologies and include mappings between element of ontologiesMapping pattern is a graph structurenodes are concepts, relations or instancesEdges are mappings or relation between (domain, range) elements or structural relations between classes (subclasses, siblings)</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mapping patterns - examplesThe simplest one</p><p>Parent-child triangle</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mapping patterns - examplesMapping along taxonomy</p><p>Sibling-sibling triangle</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mapping patterns - usageMining knowledge about habits?Enhance Ontology Mapping?</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*4ft-MinerProcedure from the LISp-Miner data mining systemThis procedure mines for association rules , where , is antecedent is succedent are condition is 4ft-quantifier statistical or heuristic test over the four-fold contingency table of and .</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mining over Mapping Results - dataData matrix</p><p>Name of mapping systemName of elements in mappingTypes of elements (c, dp, op)Validity of the correspondenceOntologies where elements belong toTypes of ontologies (tool, insider, web)Manual label correctness (+, -, ?)Information about patterns in which this mapping plays role Measure and result of the other mapping from pattern</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mining over Mapping Results analytic questions1. Which systems give higher/lower validity than others to the mappings that are deemed in/correct?2. Which systems produce certain mapping patterns more often than others?3. Which systems are more succesful on certain types of ontologies?</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Mining over Mapping ResultsOutput:Ad 1)Falcon system: twice more often incorrect mappings with medium validity than all systems (on average)RiMOM and HMatch systems: more correct mappings with high validity than all system (on average)</p><p>Ad 2)HMatch: its mappings with medium validity more likely instantiate Pattern 1 than with all validity values of such correspondencesRiMOM: its mappings with high validity more likely instantiate Pattern 2 than with all validity values of such correspondences</p><p>Ad 3)Automs: has more correct mappings between ontologies which are developed according to web-pages, than all systems (on average)OWL-CtxMatch: has more correct mappings between ontologies which are developed by insiders, than all systems (on average)</p><p>on average relates to average difference: a(a+b+c+d)/((a+b)(a+c))- 1</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Graph-based methodsfor Ontology Matching (first experience)Ondej vb</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*AgendaGraph in Ontology MappingGraph Matching ProblemSimilarity FloodingStructural Method </p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Basic notation and terminologyGraphV is the set of vertices (nodes) E is the set of edges (arcs)Types of graphsDirected, undirectedAcc. To information connected with nodes and edges Labelled graphAttributed graphTree is connected graph without circleRooted tree, </p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Ontology Mapping - formal definitionOntology contains entities={concepts, relations and instances}Ontologies O1, O2 consider as directed cyclic graphs with labelled edges, labelled nodes</p><p>Alignment A is the set of mapped pairs (a,b), where a N1 and b N2.</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Simplifacation example1Consider just subclass/superclass relation, without multiple inheritanceOntologies as rooted trees</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Labels of concepts example1</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Suggested structure-based techniqueOnto2TreeExactMatch -&gt; initial mapping (s:Thing=t:Thing)PropagateInitMappings using structures of trees and initial mappings to deduce new subsumption relations</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*New subsumptions example1</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Graph Matching Problem Graph are used in many fields (effective way of representing objects)Exact graph matching (isomorphism)</p><p>Inexact graph matching (homomorphism)</p><p>One-to-oneMany-to-many matching (even more difficult to solve, preferable more concrete results)</p><p>complexity problem! combinatorial nature of graph matching problem</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*How to measure the similarity between nodes and arcs? </p><p>Isomorhism in graph Graph edit distance measuresSimilarity Flooding algorithm</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*How to measure the similarity between nodes and arcs? Isomorhism in graph? Rather homomorphismTree simplification efficient algorithms exist Begin with leaves Assign the set of vertices, which might be isomorphicAccording to degree of vertices, how many leaves or nonleaves they are adjacent to Make partitions of potentially isomorphic vertices Classes of equivalence</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*How to measure the similarity between nodes and arcs? Graph edit distance measuresTree simplification againCompute the minimum cost to transform one tree into another using elementary operations, such asSubstitution (replacing label of node)Insertion (of a node)Deletion (of a node)</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Similarity Flooding algorithminput: two structure (generally)output: mappings between corresponding nodes</p><p>author: Sergey Melnik, 2001</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Similarity Flooding1. Models converted into directed labeled graphsIntuition behind:Elements of two distinct models are similar when their adjacent elements are similar2. The similarity of two elements is propagated (partly) to their respective neighbors(fixpoint computation)3. some filters are used on mappings-&gt;results</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Similarity FloodingAlgorithm1. G1=Graph(S1); G2=Graph(S2)2. initialMap = StringMatch(G1,G2)3. product = SFJoin(G1,G2,initialMap)4. result = selectThreshold(product)</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Example2 - crs_dr.owl, pcs.owlcrs_dr.owlpcs.owl</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Simple Structural methodNodes in trees represent with attributes derived from their place in treeAttributes for node sLevel(s)Length(s)Children(s)Max_children(s)Siblings(s)Max_siblings(s)</p><p>relLevel(s)relChildren(s)relSiblings(s)</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Structural MethodStructureDistance(Ontology O1, Ontology O2) S=Level_order(O1); T=Level_order(O2) //trees S=Attributes(S); T=Attributes(T) for each s in S for each t in T distance = distance(s,t) //euclidean distance in three-dimensional space</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Example3 - crs_dr.owl, pcs.owlcrs_dr.owl</p><p>for KEG seminar</p></li><li><p>*for KEG seminar*Example3 - crs_dr.owl, pcs.ow...</p></li></ul>

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