Skip to main content

A connectionist approach to the distance-based analysis of relational data

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1280))

Abstract

Objects with higher structural complexity often cannot be described by feature vectors without losing important structural information. Several types of structured objects can be represented adequately by labeled graphs. The similarity of such descriptions is difficult to define and to compute. However, many algorithms in machine learning, knowledge discovery, pattern recognition and classification are based on the estimation of the similarity between the analysed objects. In order to make similarity based algorithms like nearest neighbor classifiers, clustering, or generalised prototype learning accessible for the analysis of relational data, a connectionist approach for the determination of the similarity of arbitrary labeled graphs is introduced.

Using an example from organic chemistry, it is shown that classifiers based on the connectionist approach to structural similarity to be considered in this paper perform very satisfactorily in comparison with recent logical and feature vector approaches. Moreover, being able to handle relational data in a natural way without any loss of structural information, the algorithms need only a subset of the given features of the objects for classification.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D.W. Aha. Inductive Logic Programming, chapter Relating Relational Learning Algorithms. Academic Press, London, 1992.

    Google Scholar 

  2. Y. Akiyama et al.. Combinatorial optimization with gaussian machines. In IEEE Int. Conf. on Neural Networks, vol. I, pp. 533–540. 1989.

    Article  Google Scholar 

  3. J.E. Ash, W.A. Warr, and P. Willett. Chemical Structure Systems. Computational Techniques for Representation, Searching and Processing of Structural Information. Ellis Horwood, 1991.

    Google Scholar 

  4. J.M. Barnard. Substructure Searching Methods: Old and new. J. Chem. Inf. Comp. Sci., 33:532–538, 1993.

    Google Scholar 

  5. L.I. Burke and J.P. Ignizio. Neural networks and operations research: An overview. Computers Ops.Res., 19(3/4):179–189, 1992.

    Article  MATH  Google Scholar 

  6. L. Cinque et al.. An improved algorithm for relational distance graph matching. Pattern Recognition, 29(2):349–359, feb 1996.

    Article  Google Scholar 

  7. D.J. Cook and L.B. Holder. Substructure Discovery Using Minimum Description Length and Background Knowledge. Journal of Artificial Intelligence Research, 1:231–255, 1994.

    Google Scholar 

  8. W. Emde and D. Wettschereck. Relational instance-based learning. In L. Saitta, editor, Proc. of the 13th Int. Conf. on Machine Learning, pages 122–130. Morgan Kaufmann, 1996.

    Google Scholar 

  9. J. A. Feldman and D. H. Ballard. Computing with Connections. TR 72, University of Rochester, April 1981.

    Google Scholar 

  10. J. A. Feldman, M. A. Fanty, N. Goddard, and K. Lynne. Computing with Structured Connectionist Networks. TR 213, University of Rochester, April 1987.

    Google Scholar 

  11. D. H. Fisher. Knowledge acquisition via incremental conceptual clustering. Machine Learning, 2(2):139–172, 1987.

    Google Scholar 

  12. N. Funabiki, Y. Takefuji, and K.-C. Lee. A neural network model for finding a near-maximal clique. Journal of Parallel and Distributed Computing, 14(3):340–344, March 1992.

    Article  Google Scholar 

  13. P. Geibel, K. Schädler, and F. Wysotzki. Begriffslernen für strukturierte Objekte (Concept Learning for Relational Structures). In Proc. of FGML-95, Dortmund, Germany, 1995.

    Google Scholar 

  14. P. Geibel and F. Wysotzki. Learning relational concepts with decision trees. In L. Saitta, ed., Machine Learning: Proc. of the 13th Int. Conf., pages 166–174. Morgan Kaufmann Publishers, San Fransisco, CA, 1996.

    Google Scholar 

  15. P. Geibel and F. Wysotzki. Relational learning with decision trees. In W. Wahlster, editor, Proc. of the 12th European Conf. on Artificial Intelligence. John Wiley and Sons, Ltd., 1996.

    Google Scholar 

  16. J. H. Gennari, P. Langley, and D. Fisher. Models of Incremental Concept Formation. Artificial Intelligence, 40:11–61, 1989.

    Article  Google Scholar 

  17. J. Hopfield and D. Tank. Neural computations of decisions in optimization problems. Biological Cybernetics, 52:141–152, 1986.

    MathSciNet  Google Scholar 

  18. J.J. Hopfield. Neurons with graded response have collective computational properties like those of two-state neurons. In Proceedings of the National Academy of Sciences USA 81, pages 3088–3092. 1984.

    Google Scholar 

  19. A. Jagota. Efficiently approximating MAX-CLIQUE in a hopfield-style network. In Proc. of Int. Joint Conf. on Neural Networks '92 Vol. II, pages 248–253, 1992.

    Google Scholar 

  20. F. Kaden. Graphmetriken und Distanzgraphen. In Beiträge zur angewandten Graphentheorie, ZKI-Informationen. Berlin, Juni 1982.

    Google Scholar 

  21. J.-U. Kietz. Induktive Analyse Relationaler Daten. PhD thesis, TU Berlin, FB 13, 1996.

    Google Scholar 

  22. R. D. King, M. J. E. Sternberg, A. Srinivasan, and S. H. Muggleton. Knowledge Discovery in a Database of Mutagenic Chemicals. In Proceedings of the Workshop “Statistics, Machine Learning and Discovery in Databases” at the ECML-95, 1995.

    Google Scholar 

  23. N. Lavrac and S. Dzeroski. Inductive Logic Programming: Techniques and Applications. Ellis Horwood, New York, 1994.

    MATH  Google Scholar 

  24. C. Looi. Neural network methods in combinatorial optimization. Computers and Operations Research, 19(3/4):191–208, 1992.

    Article  MATH  Google Scholar 

  25. D. G. Lowe. Similarity metric learning for a variable-kernel classifier. UBC-TR-93-43, University of British Columbia, Vancouver, November 1993.

    Google Scholar 

  26. H. Mannila. Aspects of data mining. In Proceedings of the Workshop “Statistics, Machine Learning and Discovery in Databases” at the ECML-95, 1995.

    Google Scholar 

  27. M. Moulet and Y. Kodratoff. From machine learning towards knowledge discovery in databases. In Proceedings of the Workshop “Statistics, Machine Learning and Discovery in Databases” at the ECML-95, 1995.

    Google Scholar 

  28. K. Schädler, U. Schmid, B. Machenschalk, and H. Lübben. A neural net for determining structural similarity of recursive programs. In R. Bergmann and W. Wilke, eds., Proc. of the German Workshop of Case-Based Reasoning, pages 199–206, Technical Report Univ. of Kaiserslautern, LSA-97-01E, Kaiserslautern, 1997.

    Google Scholar 

  29. K. Schädler and F. Wysotzki. Klassifizierungslernen mit Hilfe spezieller Hopfield-Netze. In W. Dilger, M. Schlosser, J. Zeidler, and A. Ittner, eds., Beiträge zum 9.Fachgruppentreffen ”Maschinelles Lernen”, number CSR-96-06 in Chemnitzer Informatik-Berichte, pages 96–100. TU Chemnitz-Zwickau, August 1996.

    Google Scholar 

  30. K. Schädler and F. Wysotzki. Theoretical foundations of a special neural net approach for graphmatching. Technical Report 96-26, TU Berlin, CS Dept., 1996.

    Google Scholar 

  31. K. Schädler and F. Wysotzki. A connectionist approach to structural similarity determination as a basis of clustering, classification and feature detection. In Proc. of the 1st European Symposium on the Principles of Data Mining and Knowledge Discovery, LNAI. Springer, to appear 1997.

    Google Scholar 

  32. T. Scheffer, R. Herbrich, and F. Wysotzki. Efficient θ-subsumption based on graph algorithms. In W. Dilger, M. Schlosser, J. Zeidler, and A. Ittner, eds., Beiträge zum 9.Fachgruppentreffen ”Maschinelles Lernen”, number CSR-96-06 in Chemnitzer Informatik-Berichte, pages 96–100. TU Chemnitz-Zwickau, august 1996.

    Google Scholar 

  33. L.G. Shapiro and R.M. Haralick. A metric for comparing relational descriptions. IEEE Trans.Pattern Anal. Mach.Intell., 7(1):90–94, 1985.

    Article  Google Scholar 

  34. B. W. Silverman. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London New York, 1986.

    Book  MATH  Google Scholar 

  35. A. Voß. Similarity concepts and retrieval methods. FABEL Report 13, GMD, Sankt Augustin, 1994.

    Google Scholar 

  36. Jun Wang. Progress in Neural Networks, volume 3, chapter 11: Deterministic Neural Networks for Combinatorial Optimization, pages 319–340. Ablex Publishing Corporation, Norwood, New Jersey, 1995.

    Google Scholar 

  37. Ch. Wisotzki and F. Wysotzki. Prototype, nearest neighbor and hybrid algorithms for time series classification. In N. Lavrac and S.Wrobel, editors, Machine Learning: ECML-95, number 912 in LNAI, pages 364–367. Springer, 1995.

    Google Scholar 

  38. F. Wysotzki. Artificial Intelligence and Artificial Neural Nets. In Proc. 1st Workshop on AI, Shanghai, September 1990. TU Berlin and Jiao Tong Univ. Shanghai.

    Google Scholar 

  39. F. Wysotzki. Artificial intelligence and artificial neural nets. In L. Budach, editor, Neural Informatics., number 12/1989 in Informatik Informationen Reporte, pages 43–51, Berlin, 1989. Akademie der Wissenschaften der DDR.

    Google Scholar 

  40. B. Zelinka. On a certain distance between isomorphism classes of graphs. Casopis pro pêstováni matematiky, 100:371–373, 1975.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Xiaohui Liu Paul Cohen Michael Berthold

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag

About this paper

Cite this paper

Schädler, K., Wysotzki, F. (1997). A connectionist approach to the distance-based analysis of relational data. In: Liu, X., Cohen, P., Berthold, M. (eds) Advances in Intelligent Data Analysis Reasoning about Data. IDA 1997. Lecture Notes in Computer Science, vol 1280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052836

Download citation

  • DOI: https://doi.org/10.1007/BFb0052836

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63346-4

  • Online ISBN: 978-3-540-69520-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics