1. 4/17/2015for KEG seminar1 A posteriori evaluation of Ontology Mapping results Graph-based methods for Ontology Matching Ondřej Šváb KIZI

2. 4/17/2015for KEG seminar2 Agenda  Conference track within OAEI-2006 Initial manual empirical evaluation  Empirical Evaluation via Logical Reasoning Mapping debugging based on Drago system Experiments with OntoFarm collection  Consensus Building Workshop  Mining over the mappings with meta-data

3. 4/17/2015for KEG seminar3 Agenda  Conference track within OAEI-2006 Initial manual empirical evaluation  Empirical Evaluation via Logical Reasoning Mapping debugging based on Drago system Experiments with OntoFarm collection  Consensus Building Workshop  Mining over the mappings with meta-data

4. 4/17/2015for KEG seminar4 Conference track - Features  Broadly understandable domain Conference organisation  Free exploration by participants within 10 ontologies  No a priori reference alignment  Participants: 6 research groups

5. 4/17/2015for KEG seminar5 Conference track - Dataset http://nb.vse.cz/~svabo/oaei2006/index2.html OntoFarm collection

6. 4/17/2015for KEG seminar6 Conference track - Participants  6 participants Automs Coma++ OWL-CtxMatch Falcon HMatch RiMOM

7. 4/17/2015for KEG seminar7 Conference track - Goals  Focus on interesting mappings and unclear mappings Why should they be mapped?  Arguments: against and for Which systems did discover them? Differences in similarity measures  Underlying techniques?

8. 4/17/2015for KEG seminar8 Evaluation  Processing all mappings by hand  Assessment 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

9. 4/17/2015for KEG seminar9 Evaluation…  Subsumption mistaken for equivalence Author,Paper_Author Conference_Trip, Conference_part  Inverse property has_author,authorOf  Siblings mistaken for equivalence ProgramCommittee,Technical_commitee  Lexical confusion error program,Program_chair  Relation – Class mapping has_abstract,Abstract Topic,coversTopic; read_paper,Paper

10. 4/17/2015for KEG seminar10 Evaluation…  Some statistics as a side-effect of processing

11. 4/17/2015for KEG seminar11 Evaluation…

12. 4/17/2015for KEG seminar12 Agenda  Conference track within OAEI-2006 Initial manual empirical evaluation  Empirical Evaluation via Logical Reasoning Mapping debugging based on Drago system Experiments with OntoFarm collection  Consensus Building Workshop  Mining over the mappings with meta-data

13. 4/17/2015for KEG seminar13 Mapping debugging  Goal: to improve the quality of automatically generated mapping sets using logical reasoning about mappings  Prototype of the debugger/minimezer implemented on top of the DRAGO DDL reasoner  Semi-automatic process

14. 4/17/2015for KEG seminar14 Drago – Distributed Reasoning Architecture for Galaxy of Ontologies  Tool for distributed reasoning Based on DDL (Distributed Description Logics)  Services check ontology consistency, build classification, verify concepts satisfiability, check entailment  Resource: [http://drago.itc.it/]

15. 4/17/2015for KEG seminar15 DDL  Representation framework for semantically connected ontologies Extension of Description Logics (local interpretation, distributed,…) Distributed T-box  Semantic relations represented via directed bridge- rules: bridge rules: From the point of view of ontology j

16. 4/17/2015for KEG seminar16 DDL inference mechanism  Extension of tableau algorithm  Inference of „new“ subsumption via ‘subsumption propagation mechanism’  And its generalized form with disjunctions,…

17. 4/17/2015for KEG seminar17 Drago - architecture DRP=Drago Reasoning Peerpeer-peer network of DRPs

18. 4/17/2015for KEG seminar18 Drago - implementation  Ontological language OWL  Mapping between ontologies represented in C-OWL  Distributed Reasoner – extension of OWL reasoner Pellet (http://www.mindswap.org/2003/pellet/)http://www.mindswap.org/2003/pellet/  Communication amongst DRP via HTTP

19. 4/17/2015for KEG seminar19 Mapping debugging  1st 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

20. 4/17/2015for KEG seminar20 Mapping debugging  2nd step: discovering minimal conflict set Two conditions:  Set of mappings causing inconsistency and  By removing a mapping, concept is satisfiable  3rd step: debugging User feedback Removing mapping with the lowest degree of confidence Compute semantic distance of the concept names using WordNet synsets

21. 4/17/2015for KEG seminar21 Mapping debugging  4th step: minimization Removing redundant mappings It leads to minimal mappings set with all the semantics (logically-equivalent minimal version)

22. 4/17/2015for KEG seminar22 Experiments with OntoFarm  Mapping between class names  Six ontologies involved,  Results from four matching systems were analysed  Results of reasoning-based analysis:

23. 4/17/2015for KEG seminar23 Experiments with OntoFarm Interpretation: 1. the lower number of inconsistent alignments, the better quality of mappings 2. this analysis reveal non-obvious errors in mappings obivously incorrect mappingsnon-obivous errors in mappings

24. 4/17/2015for KEG seminar24 Agenda  Conference track within OAEI-2006 Initial manual empirical evaluation  Empirical Evaluation via Logical Reasoning Mapping debugging based on Drago system Experiments with OntoFarm collection  Consensus Building Workshop  Mining over the mappings with meta-data

25. 4/17/2015for KEG seminar25 Consensus Building Workshop  Discussion about interesting mappings discovered during manual and automatic evaluation Reaching agreement Why should they be mapped?  Arguments: against and for  During discussion the following order of arguments were taken into account: lexical reasons context of elements (subclasses superclasses, subproperties, superproperties), consider extensions of classes (set interpretation) Properties related to classes Axioms (more complex restrictions)

26. 4/17/2015for KEG seminar26 Ilustrative examples  Person vs. Human Against: different sets of subconcepts For: the same domain Result: YES

27. 4/17/2015for KEG seminar27 Ilustrative examples  PC_Member vs. Member_PC Who is the member of Program Committee? Ontologies have different interpretation. Either PC_Chair=Chair_PC or PC_Member=Member_PC result: PC_Chair=Chair_PC Therefore: PC_Member!=Member_PC

28. 4/17/2015for KEG seminar28 Ilustrative examples  Rejection vs. Reject Both are related to the outcome of the review of a submitted paper Their position in taxonomy reveal differences in meaning Reccommendation is input Decision is output of the process of revieving

29. 4/17/2015for KEG seminar29 Ilustrative examples  Location vs. Place Location relates to the country and city where conference is held Place relates to parts of building where particular events take place It is need to look at the range and domain restrictions of related properties: Location is domain of properties: locationOf Location is range of properties: heldIn iasted:Place is domain of properties: is_equipped_by sigkdd:Place is range of properties: can_stay_in

30. 4/17/2015for KEG seminar30 Lessons learned  Relevance of context Lexical matching not enough Local structure not enough? Advice: employ semantics, background knowledge (eg. Recommendation and Decision case)  Semantic relations Equivalent mappings quite often lead to inconsistencies Many concepts are closely related but not exactly the same Advice: discover not only equivalent mappings

31. 4/17/2015for KEG seminar31 Lessons learned  Alternative Interpretations (intended meaning) incomplete specification in ontologies lead to diverse interpretations (PC_Member case), Advice: check consistency of proposed mappings

32. 4/17/2015for KEG seminar32 Agenda  Conference track within OAEI-2006 Initial manual empirical evaluation  Empirical Evaluation via Logical Reasoning Mapping debugging based on Drago system Experiments with OntoFarm collection  Consensus Building Workshop  Mining over the mappings with meta-data

33. 4/17/2015for KEG seminar33 Mining over the mappings with meta-data  Introduction to Mapping Patterns  Mining 4ft-Miner Mining over Mapping Results

34. 4/17/2015for KEG seminar34 Mapping patterns  Deal with (at least) two ontologies  Reflect the structure of ontologies and include mappings between element of ontologies  Mapping pattern is a graph structure nodes are concepts, relations or instances Edges are mappings or relation between (domain, range) elements or structural relations between classes (subclasses, siblings)

35. 4/17/2015for KEG seminar35 Mapping patterns - examples  The simplest one  Parent-child triangle

36. 4/17/2015for KEG seminar36 Mapping patterns - examples  Mapping along taxonomy  Sibling-sibling triangle

37. 4/17/2015for KEG seminar37 Mapping patterns - usage  Mining knowledge about habits?  Enhance Ontology Mapping?

38. 4/17/2015for KEG seminar38 4ft-Miner  Procedure from the LISp-Miner data mining system  This 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.

39. 4/17/2015for KEG seminar39 Mining over Mapping Results - data  Data matrix Name of mapping system Name of elements in mapping Types of elements (‘c’, ’dp’, ‘op’) Validity of the correspondence Ontologies where elements belong to Types 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

40. 4/17/2015for KEG seminar40 Mining over Mapping Results – analytic questions  1. 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?

41. 4/17/2015for KEG seminar41 Mining over Mapping Results  Output:  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)  Ad 2) HMatch: its mappings with medium validity more likely instantiate Pattern 1 than with all validity values of such correspondences RiMOM: its mappings with high validity more likely instantiate Pattern 2 than with all validity values of such correspondences  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)  ‘on average’ relates to average difference: a(a+b+c+d)/((a+b)(a+c))- 1

42. 4/17/2015for KEG seminar42 Graph-based methods for Ontology Matching (first experience) Ondřej Šváb

43. 4/17/2015for KEG seminar43 Agenda  Graph in Ontology Mapping  Graph Matching Problem  Similarity Flooding  Structural Method

44. 4/17/2015for KEG seminar44 Basic notation and terminology  Graph V is the set of vertices (nodes) E is the set of edges (arcs)  Types of graphs Directed, undirected Acc. To information connected with nodes and edges  Labelled graph  Attributed graph  Tree is connected graph without circle Rooted tree, …

45. 4/17/2015for KEG seminar45 Ontology Mapping - formal definition  Ontology contains entities={concepts, relations and instances}  Ontologies O1, O2 consider as directed cyclic graphs with labelled edges, labelled nodes Alignment A is the set of mapped pairs (a,b), where a N 1 and b N 2.

46. 4/17/2015for KEG seminar46 Simplifacation – example1 Consider just subclass/superclass relation, without multiple inheritance Ontologies as rooted trees

47. 4/17/2015for KEG seminar47 Labels of concepts – example1

48. 4/17/2015for KEG seminar48 Suggested structure-based technique  Onto2Tree  ExactMatch -> initial mapping (s:Thing=t:Thing)  PropagateInitMappings – using structures of trees and initial mappings to deduce new subsumption relations  …

49. 4/17/2015for KEG seminar49 New subsumptions – example1

50. 4/17/2015for KEG seminar50 Graph Matching Problem  Graph are used in many fields (effective way of representing objects)  Exact graph matching (isomorphism)  Inexact graph matching (homomorphism) One-to-one Many-to-many matching (even more difficult to solve, preferable more concrete results)  complexity problem! – combinatorial nature of graph matching problem

51. 4/17/2015for KEG seminar51 How to measure the similarity between nodes and arcs?  Isomorhism in graph  Graph edit distance measures  Similarity Flooding algorithm

52. 4/17/2015for KEG seminar52 How to measure the similarity between nodes and arcs? Isomorhism in graph? Rather homomorphism  Tree simplification – efficient algorithms exist Begin with leaves Assign the set of vertices, which might be isomorphic  According to degree of vertices, how many leaves or nonleaves they are adjacent to Make partitions of potentially isomorphic vertices  Classes of equivalence

53. 4/17/2015for KEG seminar53 How to measure the similarity between nodes and arcs?  Graph edit distance measures Tree simplification again Compute the minimum cost to transform one tree into another using elementary operations, such as  Substitution (replacing label of node)  Insertion (of a node)  Deletion (of a node)

54. 4/17/2015for KEG seminar54 Similarity Flooding algorithm input: two structure (generally) output: mappings between corresponding nodes author: Sergey Melnik, 2001

55. 4/17/2015for KEG seminar55 Similarity Flooding  1. Models converted into directed labeled graphs  Intuition behind: Elements of two distinct models are similar when their adjacent elements are similar 2. The similarity of two elements is propagated (partly) to their respective neighbors (fixpoint computation) 3. some filters are used on mappings->results

56. 4/17/2015for KEG seminar56 Similarity Flooding  Algorithm 1. G1=Graph(S1); G2=Graph(S2) 2. initialMap = StringMatch(G1,G2) 3. product = SFJoin(G1,G2,initialMap) 4. result = selectThreshold(product)

57. 4/17/2015for KEG seminar57 Example2 - crs_dr.owl, pcs.owl crs_dr.owl pcs.owl

58. 4/17/2015for KEG seminar58 Simple Structural method  Nodes in trees represent with attributes derived from their place in tree  Attributes for node s Level(s) Length(s) Children(s) Max_children(s) Siblings(s) Max_siblings(s) relLevel(s) relChildren(s) relSiblings(s)

59. 4/17/2015for KEG seminar59 Structural Method StructureDistance(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

60. 4/17/2015for KEG seminar60 Example3 - crs_dr.owl, pcs.owl  crs_dr.owl

61. 4/17/2015for KEG seminar61 Example3 - crs_dr.owl, pcs.owl  pcs.owl

62. 4/17/2015for KEG seminar62 Example3 - crs_dr.owl, pcs.owl  Euclidean distance for some pairs in three-dimensional space

63. 4/17/2015for KEG seminar63 Example3 - crs_dr.owl, pcs.owl onto1,onto2, name1, name2, structure, sf2

64. 4/17/2015for KEG seminar64 Thank you for your attention!