Skip to main content
SpringerLink
Log in
Book cover

Advanced Course on Artificial Intelligence

ACAI 1999: Machine Learning and Its Applications pp 71–101Cite as

Function Decomposition in Machine Learning

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2049))

Abstract

To solve a complex problem, one of the effective general approaches is to decompose it into smaller, less complex and more manageable subproblems. In machine learning, this principle is a foundation for structured induction [44]: instead of learning a single complex classification rule from examples, define a concept hierarchy and learn rules for each of the (sub)concepts. Shapiro [44] used structured induction for the classification of a fairly complex chess endgame and demonstrated that the complexity and comprehensiveness (“brain-compatibility”) of the obtained solution was superior to the unstructured one. Shapiro was helped by a chess master to structure his problem domain. Typically, applications of structured induction involve a manual development of the hierarchy and a manual selection and classification of examples to induce the subconcept classification rules; usually this is a tiresome process that requires an active availability of a domain expert over long periods of time. Therefore, it would be very desirable to automate the problem decomposition task.

This is a preview of subscription content, 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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. L. Ashenhurst. The decomposition of switching functions. Technical report, Bell Laboratories BL-1(11), pages 541–602, 1952.

    Google Scholar 

  2. A. W. Biermann, J. Fairfield, and T. Beres. Signature table systems and learning. IEEE Transactions on Systems, Man and Cybernetics, 12(5):635–648, 1982.

    Article  MATH  Google Scholar 

  3. M. Bohanec, I. Bratko, and V. Rajkovič. An expert system for decision making. In H. G. Sol, editor, Processes and Tools for Decision Support. North-Holland, 1983.

    Google Scholar 

  4. M. Bohanec, B. Cestnik, and V. Rajkovič. A management decision support system for allocating housing loans. In P. Humphreys, L. Bannon, A. McCosh, and P. Migliarese, editors, Implementing System for Supporting Management Decisions, pages 34–43. Chapman & Hall, London, 1996.

    Google Scholar 

  5. M. Bohanec and V. Rajkovič. Knowledge acquisition and explanation for multi-attribute decision making. In 8th Intl Workshop on Expert Systems and their Applications, pages 59–78, Avignon, France, 1988.

    Google Scholar 

  6. M. Bohanec and V. Rajkovič. DEX: An expert system shell for decision support. Sistemica, 1(1):145–157, 1990.

    Google Scholar 

  7. I. Bratko, I. Mozetič, and N. Lavrač. KARDIO: a study in deep and qualitative knowledge for expert systems. MIT Press, 1989.

    Google Scholar 

  8. N. H. Bshouty, T. R. Hancock, and L. Hellerstein. Learning boolean read-once formulas over generalized bases. Journal of Computer and System Sciences, 50(3):521–542, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  9. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, 1989.

    Google Scholar 

  10. H. A. Curtis. A New Approach to the Design of Switching Functions. Van Nostrand, Princeton, N.J., 1962.

    Google Scholar 

  11. J. Demšar, B. Zupan, M. Bohanec, and I. Bratko. Constructing intermediate concepts by decomposition of real functions. In M. van Someren and G. Widmer, editors, Proc. European Conference on Machine Learning, ECML-97, pages 93–107, Prague, April 1997. Springer.

    Google Scholar 

  12. J. Efstathiou and V. Rajkovič. Multiattribute decisionmaking using a fuzzy heuristic approach. IEEE Trans. on Systems, Man and Cybernetics, 9:326–333, 1979.

    Article  Google Scholar 

  13. C. Files, R. Drechsler, and M. Perkowski. Functional decomposition of MVL functions using multi-valued decision diagrams. In International Symposium on Multi-Valued Logic, may 1997.

    Google Scholar 

  14. J. A. Goldman. Pattern theoretic knowledge discovery. In Proc. the Sixth Int’l IEEE Conference on Tools with AI, 1994.

    Google Scholar 

  15. T. R. Hancock, M. Golea, and M. Marchand. Learning nonoverlaping perceptron networks from examples and membership queries. Machine Learning, 16(3):161–183, 1994.

    Google Scholar 

  16. R. Kohavi. Bottom-up induction of oblivious read-once decision graphs. In F. Bergadano and L. de Raedt, editors, Proc. European Conference on Machine Learning, pages 154–169. Springer-Verlag, 1994.

    Google Scholar 

  17. I. Kononenko. Estimating attributes: Analysis and extensions of RELIEF. In F. Bergadano and L. de Raedt, editors, Proceedings of the European Conference on Machine Learning, pages 171–182. Springer-Verlag, 1994.

    Google Scholar 

  18. I. Kononenko, E. šimec, and M. Robnik šikonja. Overcoming the myopia of inductive learning algorithms with ReliefF. Applied Intelligence Journal, 7(1):39–56, 1997.

    Article  Google Scholar 

  19. Y.-T. Lai, K.-R. R. Pan, and M. Pedram. OBDD-based function decomposition: Algorithms and implementation. IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, 15(8):977–990, 1996.

    Article  Google Scholar 

  20. Y.-T. Lai, M. Pedram, and S. Sastry. BDD-based decomposition of logic functions with application to FPGA synthesis. In 30th DAC, pages 642–647, 1993.

    Google Scholar 

  21. T. Luba. Decomposition of multiple-valued functions. In 25th Intl. Symposium on Multiple-Valued Logic, pages 256–261, Bloomigton, Indiana, May 1995.

    Google Scholar 

  22. T. Luba and H. Selvaraj. A general approach to boolean function decomposition and its application in FPGA-based synthesis. VLSI Design, 3(3-4):289–300, 1995.

    Article  Google Scholar 

  23. R. S. Michalski. A theory and methodology of inductive learning. In R. Michalski, J. Carbonnel, and T. Mitchell, editors, Machine Learning: An Artificial Intelligence Approach, pages 83–134. Kaufmann, Paolo Alto, CA, 1983.

    Google Scholar 

  24. R. S. Michalski. Understanding the nature of learning: Issues and research directions. In R. Michalski, J. Carbonnel, and T. Mitchell, editors, Machine Learning: An Artificial Intelligence Approach, pages 3–25. Kaufmann, Los Atlos, CA, 1986.

    Google Scholar 

  25. D. Michie. Problem decomposition and the learning of skills. In N. Lavrač and S. Wrobel, editors, Machine Learning: ECML-95, Notes in Artificial Intelligence 912, pages 17–31. Springer-Verlag, 1995.

    Google Scholar 

  26. I. Mozetič. Learning of qualitative models. In I. Bratko and N. Lavrač, editors, Progress in Machine Learning. Sigma Press, 1987. Wilmslow, England.

    Google Scholar 

  27. I. Mozetič. The role of abstractions in learning of qualitative models. In Proc. Fourth Int. Workshop on Machine Learning. Morgan Kaufmann, 1987. Irvine, Ca.

    Google Scholar 

  28. S. Muggleton. Structuring knowledge by asking questions. In I. Bratko and N. Lavrač, editors, Progress in Machine Learning, pages 218–229. Sigma Press, 1987.

    Google Scholar 

  29. S. Muggleton. Inductive Acquisition of Expert Knowledge. Addison-Wesley, Workingham, England, 1990.

    Google Scholar 

  30. P. M. Murphy and D. W. Aha. UCI Repository of machine learning databases http://www.ics.uci.edu/~mlearn/mlrepository.html. Irvine, CA: University of California, Department of Information and Computer Science, 1994.

    Google Scholar 

  31. C. G. Nevill-Manning and I. H. Witten. Identifying hierarchical structure in sequences: A linear-time algorithm. Journal of Artificial Intelligence Research, 7:67–82, 1997.

    MATH  Google Scholar 

  32. M. Olave, V. Rajkovič, and M. Bohanec. An application for admission in public school systems. In I. Th. M. Snellen, W. B. H. J. van de Donk, and J.-P. Baquiast, editors, Expert Systems in Public Administration, pages 145–160. Elsevier Science Publishers (North Holland), 1989.

    Google Scholar 

  33. M. Perkowski and H. Uong. Automatic design of finite state machines with electronically programmable devices. In Record of Northcon’ 87, pages 16/4.1–16/4.15, Portland, OR, 1987.

    Google Scholar 

  34. B. Pfahringer. Controlling constructive induction in CiPF. In F. Bergadano and L. de Raedt, editors, Machine Learning: ECML-94, pages 242–256. Springer-Verlag, 1994.

    Google Scholar 

  35. J. R. Quinlan. C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers, 1993.

    Google Scholar 

  36. R. Quinlan. Induction of decision trees. Machine Learning, 1(1):81–106, 1986.

    Google Scholar 

  37. H. Ragavan and L. Rendell. Lookahead feature construction for learning hard concepts. In Proc. Tenth International Machine Learning Conference, pages 252–259. Morgan Kaufman, 1993.

    Google Scholar 

  38. V. Rajkovič and M. Bohanec. Decision support by knowledge explanation. In H. G. Sol and J. Vecsenyi, editors, Environments for supporting Decision Process. Elsevier Science Publishers B.V., 1991.

    Google Scholar 

  39. T. D. Ross, M. J. Noviskey, D. A. Gadd, and J. A. Goldman. Pattern theoretic feature extraction and constructive induction. In Proc. ML-COLT’ 94 Workshop on Constructive Induction and Change of Representation, New Brunswick, New Jersey, July 1994.

    Google Scholar 

  40. S. J. Russell. Tree-structured bias. In M. N. Saint Paul, editor, Proc. The Seventh National Conference on Artificial Intelligence, pages 641–645, San Mateo, CA, 1988. Morgan Kaufmann.

    Google Scholar 

  41. S. L. Salzberg. On comparing classifiers: Pitfalls to avoid and a recommended approach. Data Mining and Knowledge Discovery, 1:317–328, 1997.

    Article  Google Scholar 

  42. A. Samuel. Some studies in machine learning using the game of checkers. IBM J. Res. Develop., 3:221–229, 1959.

    MathSciNet  Google Scholar 

  43. A. Samuel. Some studies in machine learning using the game of checkers II: Recent progress. IBM J. Res. Develop., 11:601–617, 1967.

    Article  Google Scholar 

  44. A. D. Shapiro. Structured induction in expert systems. Turing Institute Press in association with Addison-Wesley Publishing Company, 1987.

    Google Scholar 

  45. A. D. Shapiro and T. Niblett. Automatic induction of classificiation rules for a chess endgame. In M. R. B. Clarke, editor, Advances in Computer Chess 3, pages 73–92. Pergamon, Oxford, 1982.

    Google Scholar 

  46. I. Stahl. An overview of predicate invention techniques in ILP. In ESPRIT BRA 6020: Inductive Logic Programming, 1991.

    Google Scholar 

  47. P. Tadepalli and S. Russell. Learning from examples and membership queries with structured determinations. Machine Learning, 32:245–295, 1998.

    Article  MATH  Google Scholar 

  48. S. B. Thrun and et al. tA performance comparison of different learning algorithms. Technical report, Carnegie Mellon University CMU-CS-91-197, 1991.

    Google Scholar 

  49. W. Wan and M. A. Perkowski. A new approach to the decomposition of incompletely specified functions based on graph-coloring and local transformations and its application to FPGA mapping. In Proc. of the IEEE EURO-DAC’ 92, pages 230–235, Hamburg, September 1992.

    Google Scholar 

  50. D. J. A. Welsh and M. B. Powell. An upper bound on the chromatic number of a graph and its application to timetabling problems. Computer Journal, 10:85–86, 1967.

    Article  MATH  Google Scholar 

  51. B. Zupan. Machine learning based on function decomposition. PhD thesis, University of Ljubljana, April 1997. Available at http://www.ai.ijs.si/BlazZupan/papers.html.

  52. B. Zupan, M. Bohanec, J. Demšar, and I. Bratko. Feature transformation by function decomposition. IEEE Intelligent Systems & Their Applications, 13(2):38–43, March/April 1998.

    Article  Google Scholar 

  53. B. Zupan, M. Bohanec, J. Demšar, and I. Bratko. Learning by discovering concept hierarchies. Artificial Intelligence, 109(1-2):211–242, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  54. B. Zupan, I. Bratko, M. Bohanec, and J. Demšar. Induction of concept hierarchies from noisy data. In P. Langley, editor, Proceedings of the Seventeenth International Conference on Machine Learning (ICML-2000), pages 1199–1206, San Francisco, CA, 2000. Morgan Kaufmann.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computer and Information Sciences, Slovenia

    Blaž Zupan, Ivan Bratko & Janez Demšar

  2. Department of Intelligent Systems, J. Stefan Institute, Jamova 39, SI-1000, Ljubljana, Slovenia

    Blaž Zupan, Ivan Bratko & Marko Bohanec

  3. Baylor College of Medicine, 1 Baylor Plaza, Houston, TX, 77030, USA

    Blaž Zupan

Authors
  1. Blaž Zupan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ivan Bratko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marko Bohanec
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Janez Demšar
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. National Centre for Scientific Research “Demokritos”, Institute of Informatics and Telecommunications, P.O. Box 60228, Ag. Paraskevi, 15310, Athens, Greece

    Georgios Paliouras , Vangelis Karkaletsis  & Constantine D. Spyropoulos ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Zupan, B., Bratko, I., Bohanec, M., Demšar, J. (2001). Function Decomposition in Machine Learning. In: Paliouras, G., Karkaletsis, V., Spyropoulos, C.D. (eds) Machine Learning and Its Applications. ACAI 1999. Lecture Notes in Computer Science(), vol 2049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44673-7_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-44673-7_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42490-1

  • Online ISBN: 978-3-540-44673-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation