1. OMEN: A Probabilistic Ontology Mapping Tool Mitra et al.

2. The Problem We need to map databases or ontologies We need to map databases or ontologies Mapping of two different ontologies

3. The Problem Mapping is difficult Mapping is difficult Most mapping tools are imprecise Most mapping tools are imprecise Even experts could be uncertain Even experts could be uncertain We deal with probabilistic mappings We deal with probabilistic mappings

4. The Solution Infer mappings based on previous ones Infer mappings based on previous ones We use Bayesian Nets for inference We use Bayesian Nets for inference We use other tools for initial distributions We use other tools for initial distributions Preliminary results are encouraging Preliminary results are encouraging

5. Basic Concepts Bayesian network: Bayesian network: Probabilistic graphical model that represents Random variables Evidence nodes: The value is given Evidence nodes: The value is given T

6. Bayesian Network Conditional Probability tables (CPT) Conditional Probability tables (CPT)

7. Bayesian Nets in our approach How do we build the Bayesian Net How do we build the Bayesian Net Nodes are property or class matches Nodes are property or class matches Classes are concepts Classes are concepts Properties are attributes of classes Properties are attributes of classes m(C 1,C 1 ’)C1C1 C1’C1’ Ontology 1Ontology 2

8. Building Bayesian Nets

9. Our Bayesian Nets All combinations of nodes is too many All combinations of nodes is too many We generate only “useful” nodes We generate only “useful” nodes The cutoff is k from evidence nodes The cutoff is k from evidence nodes Up to 10 parents per node Up to 10 parents per node Cycles are avoided (confidence ~.5) Cycles are avoided (confidence ~.5)

10. Our Bayesian Nets We need evidence nodes and CPTs We need evidence nodes and CPTs Evidence nodes come from initialization Evidence nodes come from initialization CPTs come from Meta-rules CPTs come from Meta-rules

11. Meta-rules Describes how other rules should be used Describes how other rules should be used Basic Meta-rule Basic Meta-rule m(C 1,C 1 ’)C1C1 C1’C1’ m(C 2,C 2 ’)C2C2 C2’C2’ qq’ P 1 =x P 2 =x+c

12. Other Meta-rules Range: Restriction of property values Range: Restriction of property values Mappings between properties and ranges of properties Mappings between properties and ranges of properties Single range Single range Specialization Specialization

13. Other Meta-rules Mappings between super classes Mappings between super classes Children matching depends on parents matching Fixed Influence Method (FI): P=.9 Fixed Influence Method (FI): P=.9 Initial Probability Method (AP): P= y+c Initial Probability Method (AP): P= y+c Parent Probability Method (PP): P= x+c Parent Probability Method (PP): P= x+c

14. Probability Distribution Probability Distribution for mapping between C and C’

15. Combining Influences We assume that the parents are conditionally independent We assume that the parents are conditionally independent P[C|A,B] = P[C|A] x P[C|B] P[C|A,B] = P[C|A] x P[C|B] Fix of this for future work Fix of this for future work

16. Results 2 Sets of 11 and 19 nodes 2 Sets of 11 and 19 nodes Predicate matching was manual Predicate matching was manual Thresholds were.85 and.15 Thresholds were.85 and.15

17. Results

18. Strengths Innovative research Innovative research Published at ISWC Published at ISWC Mathematically oriented Mathematically oriented

19. Weaknesses Lots of typos Lots of typos No comparison with current methods No comparison with current methods Little literature research Little literature research Could use better explanation of basic concepts Could use better explanation of basic concepts

20. Future Work Handling conditionally dependency of parent nodes Handling conditionally dependency of parent nodes Handling of matching predicates Handling of matching predicates Automatic pruning and building of the network Automatic pruning and building of the network

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