Skip to main content
SpringerLink
Log in

Refinement-Based Similarity Measures for Directed Labeled Graphs

  • Conference paper
  • First Online:
Case-Based Reasoning Research and Development (ICCBR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9969))

Included in the following conference series:

Abstract

This paper presents a collection of similarity measures based on refinement operators for directed labeled graphs (DLGs). We build upon previous work on refinement operators for other representation formalisms such as feature terms and description logics. Specifically, we present refinement operators for DLGs, which enable the adaptation of three similarity measures to DLGs: the anti-unification-based, \(S_{\lambda }\), the property-based, \(S_{\pi }\), and the weighted property-based, \(S_{w\pi }\), similarities. We evaluate the resulting measures empirically comparing them to existing similarity measures for structured data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A Refinement-Operator Library for Directed Labeled Graphs: https://github.com/santiontanon/RHOG.

  2. 2.

    A graph trivially subsumes itself with the mapping \(m(v) = v\).

  3. 3.

    If a graph \(g_1\) subsumes \(g_2\) through a mapping \(m_1\), and \(g_2\) subsumes \(g_3\) through a mapping \(m_2\), then we know \(g_1\) subsumes \(g_3\) via the mapping \(m(v) = m_2(m_1(v))\).

  4. 4.

    Notice that it is possible to compute the remainder without the need to actually perform any type of unification operation, which can be computationally expensive.

  5. 5.

    Datasets can be downloaded in dot, GML and GraphML format from https://github.com/santiontanon/RHOG.

  6. 6.

    http://www.doc.ic.ac.uk/~shm/progol.html.

References

  1. Aamodt, A., Plaza, E.: Case-based reasoning: foundational issues, methodological variations, and system approaches. Artif. Intell. Commun. 7(1), 39–59 (1994)

    Google Scholar 

  2. Armengol, E., Plaza, E.: Relational case-based reasoning for carcinogenic activity prediction. Artif. Intell. Rev. 20(1–2), 121–141 (2003)

    Article  Google Scholar 

  3. Bergmann, R., Stahl, A.: Similarity measures for object-oriented case representations. In: Smyth, B., Cunningham, P. (eds.) EWCBR 1998. LNCS, vol. 1488, pp. 25–36. Springer, Heidelberg (1998). doi:10.1007/BFb0056319

    Chapter  Google Scholar 

  4. Bille, P.: A survey on tree edit distance and related problems. Theoret. Comput. Sci. 337(1), 217–239 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bisson, G.: Learing in FOL with a similarity measure. In: Proceedings of AAAI 1992, pp. 82–87 (1992)

    Google Scholar 

  6. d’Amato, C.: Similarity-based learning methods for the semantic web. Ph.D. thesis, Università degli Studi di Bari (2007)

    Google Scholar 

  7. Emde, W., Wettschereck, D.: Relational instance based learning. In: Saitta, L. (ed.) Machine Learning - Proceedings 13th International Conference on Machine Learning, pp. 122–130. Morgan Kaufmann Publishers (1996)

    Google Scholar 

  8. Fanizzi, N., d’Amato, C., Esposito, F.: Induction of optimal semi-distances for individuals based on feature sets. In: Proceedings of 2007 International Workshop on Description Logics, CEUR-WS (2007)

    Google Scholar 

  9. Fanizzi, N., d’Amato, C., Esposito, F.: Learning with Kernels in description logics. In: Železný, F., Lavrač, N. (eds.) ILP 2008. LNCS (LNAI), vol. 5194, pp. 210–225. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85928-4_18

    Chapter  Google Scholar 

  10. Ferilli, S., Fanizzi, N., Di Mauro, N., Basile, T.M.: Efficient theta-subsumption under object identity. In: Workshop AI*IA 2002, pp. 59–68 (2002)

    Google Scholar 

  11. Gabel, T.: Learning similarity measures: strategies to enhance the optimisation process. Diploma thesis, kaiserslautern university of technology (2003)

    Google Scholar 

  12. Gärtner, T., Lloyd, J.W., Flach, P.A.: Kernels for structured data. In: Matwin, S., Sammut, C. (eds.) ILP 2002. LNCS (LNAI), vol. 2583, pp. 66–83. Springer, Heidelberg (2003). doi:10.1007/3-540-36468-4_5

    Chapter  Google Scholar 

  13. González-Calero, P.A., Díaz-Agudo, B., Gómez-Albarrán, M.: Applying DLs for retrieval in case-based reasoning. In: Proceedings of the 1999 Description Logics Workshop (DL 1999) (1999)

    Google Scholar 

  14. Hutchinson, A.: Metrics on terms and clauses. In: Someren, M., Widmer, G. (eds.) ECML 1997. LNCS, vol. 1224, pp. 138–145. Springer, Heidelberg (1997). doi:10.1007/3-540-62858-4_78

    Chapter  Google Scholar 

  15. Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized Kernels between labeled graphs. In: Proceedings of the Twentieth International Conference (ICML 2003), pp. 321–328. AAAI Press (2003)

    Google Scholar 

  16. van der Laag, P.R.J., Nienhuys-Cheng, S.H.: Completeness and properness of refinement operators in inductive logic programming. J. Logic Program. 34(3), 201–225 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Larson, J., Michalski, R.S.: Inductive inference of VL decision rules. SIGART Bull. 63(63), 38–44 (1977)

    Article  Google Scholar 

  18. Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Sov. Phys. Dokl. 10, 707–710 (1966)

    MathSciNet  MATH  Google Scholar 

  19. Nienhuys-Cheng, S.-H.: Distance between herbrand interpretations: a measure for approximations to a target concept. In: Lavrač, N., Džeroski, S. (eds.) ILP 1997. LNCS, vol. 1297, pp. 213–226. Springer, Heidelberg (1997). doi:10.1007/3540635149_50

    Chapter  Google Scholar 

  20. Ontanón, S., Plaza, E.: Similarity measures over refinement graphs. Mach. Learn. 87, 57–92 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Ontañón, S.: RHOG: a refinement-operator library for directed labeled graphs. arXiv preprint cs.AI (2016). http://arxiv.org/abs/1604.06954

  22. Ontañón, S., Plaza, E.: Refinement-based disintegration: an approach to re-representation in relational learning. AI Commun. 28(1), 35–46 (2015)

    MathSciNet  Google Scholar 

  23. Ramon, J.: Clustering and instance based learning in first order logic. AI Commun. 15(4), 217–218 (2002)

    Google Scholar 

  24. Sánchez, D., Batet, M., Isern, D., Valls, A.: Ontology-based semantic similarity: a new feature-based approach. Expert Syst. Appl. 39(9), 7718–7728 (2012)

    Article  Google Scholar 

  25. Sánchez-Ruiz, A.A., Ontañón, S.: Least common subsumer trees for plan retrieval. In: Lamontagne, L., Plaza, E. (eds.) ICCBR 2014. LNCS (LNAI), vol. 8765, pp. 405–419. Springer, Heidelberg (2014). doi:10.1007/978-3-319-11209-1_29

    Google Scholar 

  26. Sánchez-Ruiz, A.A., Ontañón, S., González-Calero, P.A., Plaza, E.: Refinement-based similarity measure over DL conjunctive queries. In: Delany, S.J., Ontañón, S. (eds.) ICCBR 2013. LNCS (LNAI), vol. 7969, pp. 270–284. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39056-2_20

    Chapter  Google Scholar 

  27. Wolf, M., Petridis, M.: Measuring similarity of software designs using graph matching for CBR. In: Workshop Proceedings of AISEW 2008 at ECAI 2008. IOS Press (2008)

    Google Scholar 

Download references

Acknowledgements

This research was supported by grant IIS-1551338 from the National Science Foundation (NSF).

Author information

Authors and Affiliations

  1. Computer Science Department, Drexel University, Philadelphia, PA, USA

    Santiago Ontañón & Ali Shokoufandeh

Authors
  1. Santiago Ontañón
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Shokoufandeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Santiago Ontañón .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology , Atlanta, Georgia, USA

    Ashok Goel

  2. Universidad Complutense de Madrid , Madrid, Spain

    M Belén Díaz-Agudo

  3. University of West London , London, United Kingdom

    Thomas Roth-Berghofer

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Ontañón, S., Shokoufandeh, A. (2016). Refinement-Based Similarity Measures for Directed Labeled Graphs. In: Goel, A., Díaz-Agudo, M., Roth-Berghofer, T. (eds) Case-Based Reasoning Research and Development. ICCBR 2016. Lecture Notes in Computer Science(), vol 9969. Springer, Cham. https://doi.org/10.1007/978-3-319-47096-2_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-47096-2_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47095-5

  • Online ISBN: 978-3-319-47096-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation