Block Matching for Ontologies

1. Block Matching for Ontologies Wei Hu and Yuzhong QuSchool of Computer Science and Engineering, Southeast University, P.R. China XObjects Group - Southeast University

2. Outline • Introduction • Overview of the Approach • Relatedness among Domain Entities • Partitioning for Block Matching • Evaluation • Related Work • Concluding Remarks XObjects Group - Southeast University

3. Introduction • Ontology matching • Enabling interoperability among different but related ontologies • In practice, establishing mappings between domain entities • Block matching • The common relationship cardinality of mappings is 1:1. • However, mappings between sets of domain entities are more pervasive. • A block is a set of domain entities. • A block mapping is a pair of matched blocks from different ontologies. • Block matching is the process of discovering block mappings. XObjects Group - Southeast University

4. Introduction - Examples • From a microcosmic angle of view • Given two ontologies O1 and O2, O1 contains three domain entities Month, Day, Year; while O2 contains a single domain entity Date. It is more natural to match the block {Month, Day, Year} in O1 with the block {Date} in O2. • From a macroscopic angle of view • Block matching provides a general picture at a higher level to explore the correspondences between the main topics of ontologies. XObjects Group - Southeast University

5. Introduction (Cont’d.) • The block matching problem  a special partitioning problem • All the block mappings compose a partitioning of all the domain entities from the two given ontologies. • The partitioning quality – cohesiveness & coupling • In addition, the mapping quality is inherently difficult to guarantee. • At present, most of the algorithms proposed in literature are targeted to find 1:1 mappings. • One exception – PBM • Only coping with mappings between classes – not a general solution • The mapping quality is not good enough for complicated ontologies. XObjects Group - Southeast University

6. Introduction – Our Approach • So, we propose a new partitioning-based approach to address the block matching problem. • The relatedness measure – Virtual Documents • Novelty – both the mapping quality & the partitioning quality can be guaranteed simultaneously. • The partitioning algorithm – A Hierarchical Bisection Algorithm • Novelty – providing block mappings at different levels of granularity. • Flat partitioning – extracting the optimal mappings with a given number of block mappings. XObjects Group - Southeast University

7. Overview of the Approach • Our approach starts with two ontologies as input, and then after four processing stages, the output returns block mappings. • Constructing virtual documents for domain entities • Computing relatedness among domain entities • Partitioning by a hierarchical bisection algorithm • Extracting the optimal block mappings XObjects Group - Southeast University

8. Onto1 Onto2 A Toy Example XObjects Group - Southeast University

9. Step 1 – Construction of Virtual Documents • A virtual document represents a collection of weighted tokens, which reflects the intended meaning of a domain entity. • The virtual document of a domain entity contains not only the local descriptions but also the neighboring information. • Local description – for a literal node / a URIref / a blank node • Neighboring information – subject / predicate / object neighbors XObjects Group - Southeast University

10. Step 2 – Computation of Relatedness • The similarity between virtual documents is measured by the Cosine value between two vectors, corresponding to the two virtual documents in the Vector Space Model. • Generating a relatedness matrix by computing the similarity among virtual documents within each of the two ontologies as well as crossing the two ontologies. • Both of linguistic and structural relatedness within each of the two ontologies are reflected in W11 and W22. • Linguistic relatedness crossing ontologies is characterized by W12. XObjects Group - Southeast University

11. Illustration by the Toy Example • VD(onto1:Report) • Local Description = “report” • Des(onto1:Reference) = “reference” • VD(onto1:Reference) • Local Description = “reference” • Des(onto1:Report) = “report”, Des(onto1:Book), Des(onto1:hasInstitution) • VD(onto2:Entry) • Local Description = “entry” • Des(onto2:Article), Des(onto2:Book), Des(onto2:hasInstitution) The relatedness between onto1:Report and onto1:Reference is revealed throughshared words (“report” & “reference”) obtained from neighboring relationship in Vector Space Model. The relatedness between onto1:Referenceand onto2:Entry is exploited by the shared words “book”, “institution”. XObjects Group - Southeast University

12. Step 3 – The Hierarchical Bisection Algorithm • The min-max cut (Mcut) function is adopted as the criterion function. • Why is a hierarchical algorithm? • It is easy to depict the partitioning for a given domain. • There may be several correct answers. • The overview of our partitioning algorithm • Input: a relatedness matrix W • It recursively bisects a matrix into two submatrices by finding the minimum Mcut. • Output: a dendrogram consisting of layers of block mappings. XObjects Group - Southeast University

13. Step 4 – Extraction of the Optimal Block Mappings • Obtaining a flat partitioning with a given number of block mappings pwhere g is the objective function: XObjects Group - Southeast University

14. Illustration by the Toy Example (Cont’d.) • The dendrogram for onto1 & onto2 is shown as follows. • If extracting 3 block mappings, then the selected ones are … √ √ √ XObjects Group - Southeast University

15. Illustration by the Toy Example (Cont’d.) XObjects Group - Southeast University

16. Evaluation – Experimental Methodology • We implement our approach in Java, called BMO. • BMO focuses on the domain entities at the conceptual level. • We evaluate the performance of BMO in three experiments: • The mapping quality of BMO • The partitioning quality of BMO • In addition, comparing BMO with PBM • For both the mapping quality and the partitioning quality XObjects Group - Southeast University

17. Evaluation – Case Study • Two pairs of ontologies – Russia12 and TourismAB • Russia12 • Russia1 – 151 classes & 76 properties • Russia2 – 162 classes & 81 properties • 85 reference alignments (1:1) • TourismAB • TourismA – 340 classes & 97 properties • TourismB – 474 classes & 100 properties • 226 reference alignments (1:1) XObjects Group - Southeast University

18. Evaluation – Evaluation Metrics • The mapping quality – observing the correctness with the variation of the number of the block mappings. • Rationale – the higher the quality of the block mappings is, the more reference alignments could be found in the block mappings. XObjects Group - Southeast University

19. Evaluation – Evaluation Metrics (Cont’d.) • The partitioning quality – comparing the computed block mappings by BMO with the manual ones set up by volunteers. • The f-measure is defined as a combination of the precision and recall. • The entropy considers the distribution of the domain entities in block mappings and reflects the overall partitioning quality. XObjects Group - Southeast University

20. Evaluation – Experimental Results • The correctness with the variation of the number of the block mappings n • The partitioning quality of BMO XObjects Group - Southeast University

21. Evaluation – Experimental Results (Cont’d.) • The comparison between BMO and PBM • The partitioning quality between the two approaches are almost the same. • But, the mapping quality of BMO is much better than the one of PBM. XObjects Group - Southeast University

22. Related Work • Ontology matching • There exist very few approaches raising the issue of block matching. • PBM – only for class hierarchies & the mapping quality isn’t good enough • In the field of schema matching • iMap – complex mapping, hard to specify the domain knowledge in some cases • Artemis – similar to our framework, but the partitioning quality isn’t so good • Ontology partitioning • Many existing works only provide a flat partitioning on a single ontology. • Our work is a hierarchical one & partitions two ontologies simultaneously. XObjects Group - Southeast University

23. Concluding Remarks • We discussed the block matching problem and suggested both the mapping quality and the partitioning quality should be considered in block matching. • We proposed a relatedness measure based on virtual documents that simultaneously importing both linguistic and structural characteristics of domain entities. • We presented a hierarchical bisection algorithm to provide block mappings at different levels of granularity. Also, we described a method to automatically extract the optimal block mappings. • We set up two kinds of metrics to evaluate of the quality of block matching. The experimental results demonstrated that our approach is feasible. XObjects Group - Southeast University

24. Concluding Remarks – Future Work • We would like to find other possible approaches to block matching, and compare them with each other. • We look forward to setting up systematic test cases for block matching. • We plan to address the block matching issue for very large ontologies. XObjects Group - Southeast University

25. Thanks for your attention! Any comment is welcome! XObjects Group - Southeast University