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Arc Consistency Projection: A New Generalization Relation for Graphs

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Conceptual Structures: Knowledge Architectures for Smart Applications (ICCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4604))

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Abstract

The projection problem (conceptual graph projection, homomorphism, injective morphism, θ-subsumption, OI-subsumption) is crucial to the efficiency of relational learning systems. How to manage this complexity has motivated numerous studies on learning biases, restricting the size and/or the number of hypotheses explored. The approach suggested in this paper advocates a projection operator based on the classical arc consistency algorithm used in constraint satisfaction problems. This projection method has the required properties : polynomiality, local validation, parallelization, structural interpretation. Using the arc consistency projection, we found a generalization operator between labeled graphs. Such an operator gives the structure of the classification space which is a concept lattice.

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References

  1. Sowa, J.F.: Conceptual structures: information processing in mind and machine. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA (1984)

    MATH  Google Scholar 

  2. Baget, J.F., Mugnier, M.L.: Extension of simple conceptual graphs: the complexity of rules and constraints. Journal of Artificial Intelligence Research 16, 425–465 (2002)

    MATH  MathSciNet  Google Scholar 

  3. Hell, P., Nesetril, J.: Graphs and homomorphism. In: Oxford Lecture Series in Mathematics and its Application, vol. 28, Oxford University Press, Oxford (2004)

    Google Scholar 

  4. Mugnier, M.L., Chein, M.: Polynomial algorithms for projection and matching. In: Pfeiffer, H.D., Nagle, T.E. (eds.) Conceptual Structures: Theory and Implementation. LNCS, vol. 754, pp. 239–251. Springer, Heidelberg (1993)

    Google Scholar 

  5. Croitoru, M., Compatangelo, E.: A combinatorial approach to conceptual graph projection checking. In: 24th Int’l Conf. of the British Computer Society’s Specialist Group on Art’l Intell, pp. 239–251. Springer, Heidelberg (2004)

    Google Scholar 

  6. Pfeiffer, H.: A comparison of different conceptual structures projection algorithms. In: ICCS 2007 (submitted, 2007)

    Google Scholar 

  7. Maloberti, J., Sebag, M.: Fast theta-subsumption with constraint satisfaction algorithms. Machine Learning 55, 137–174 (2004)

    Article  MATH  Google Scholar 

  8. Zaki, M.: Efficiently mining frequent trees in a forest. In: 8th Intl. Conf. knowledge discovery and data mining, pp. 71–80 (2002)

    Google Scholar 

  9. Cook, D.J., Holder, L.B.: Substructure discovery using minimum description length and background knowledge. Journal of Artificial Intelligence Research 1, 231–255 (1994)

    Google Scholar 

  10. Liquiere, M., Sallantin, J.: Structural machine learning with galois lattice and graphs. In: Shavlik, J.W. (ed.) ICML, pp. 305–313. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  11. Sebag, M., Rouveirol, C.: Resource-bounded relational reasoning: induction and deduction through stochastic matching. Machine Learning 38, 41–62 (2000)

    Article  MATH  Google Scholar 

  12. Bessiere, C.: Constraint propagation. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, Elsevier, Amsterdam (2006)

    Google Scholar 

  13. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer-Verlag, New York, Inc. Secaucus, NJ, USA, Translator-C. Franzke (1997)

    Google Scholar 

  14. Plotkin, G.: A note on inductive generalization. Machine Intelligence 5, 153–163 (1970)

    MathSciNet  Google Scholar 

  15. Crole, R.: Categories for Types. Cambridge Mathematical Textbooks. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  16. Weichsel, P.M.: The kronecker product of graphs. Proc. Am. Math. Soc. 13, 47–52 (1962)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. LIRMM, 161 Rue ada, 34392 Montpellier cedex 5, France

    Michel Liquiere

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  1. Michel Liquiere
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Uta Priss Simon Polovina Richard Hill

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© 2007 Springer-Verlag Berlin Heidelberg

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Liquiere, M. (2007). Arc Consistency Projection: A New Generalization Relation for Graphs. In: Priss, U., Polovina, S., Hill, R. (eds) Conceptual Structures: Knowledge Architectures for Smart Applications. ICCS 2007. Lecture Notes in Computer Science(), vol 4604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73681-3_25

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  • DOI: https://doi.org/10.1007/978-3-540-73681-3_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73680-6

  • Online ISBN: 978-3-540-73681-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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