On Merging the Fields of Neural Networks and Adaptive Data Structures to Yield New Pattern Recognition Methodologies

  • B. John Oommen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6744)

Abstract

The aim of this talk is to explain a pioneering exploratory research endeavour that attempts to merge two completely different fields in Computer Science so as to yield very fascinating results. These are the well-established fields of Neural Networks (NNs) and Adaptive Data Structures (ADS) respectively. The field of NNs deals with the training and learning capabilities of a large number of neurons, each possessing minimal computational properties. On the other hand, the field of ADS concerns designing, implementing and analyzing data structures which adaptively change with time so as to optimize some access criteria. In this talk, we shall demonstrate how these fields can be merged, so that the neural elements are themselves linked together using a data structure. This structure can be a singly-linked or doubly-linked list, or even a Binary Search Tree (BST). While the results themselves are quite generic, in particular, we shall, as a prima facie case, present the results in which a Self-Organizing Map (SOM) with an underlying BST structure can be adaptively re-structured using conditional rotations. These rotations on the nodes of the tree are local and are performed in constant time, guaranteeing a decrease in the Weighted Path Length of the entire tree. As a result, the algorithm, referred to as the Tree-based Topology-Oriented SOM with Conditional Rotations (TTO-CONROT), converges in such a manner that the neurons are ultimately placed in the input space so as to represent its stochastic distribution. Besides, the neighborhood properties of the neurons suit the best BST that represents the data.

Keywords

Learning Capability Binary Search Tree Access Probability Prima Facie Case Analyze Data Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Adel’son-Velski’i, G.M., Landis, E.M.: An algorithm for the organization of information. Sov. Math. Dokl. 3, 1259–1262 (1962)Google Scholar
  2. 2.
    Astudillo, C.A., Oommen, J.B.: A novel self organizing map which utilizes imposed tree-based topologies. In: Kurzynski, M., Wozniak, M. (eds.) Computer Recognition Systems 3. Computer Recognition, vol. 57, pp. 169–178. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Astudillo, C.A., Oommen, B.J.: On using adaptive binary search trees to enhance self organizing maps. In: Nicholson, A., Li, X. (eds.) AI 2009. LNCS, vol. 5866, pp. 199–209. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Allen, B., Munro, I.: Self-organizing binary search trees. Journal of the ACM 25, 526–535 (1978)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Arnow, D.M., Tenenbaum, A.M.: An investigation of the move-ahead-k rules. In: Proceedings of Congressus Numerantium, Proceedings of the Thirteenth Southeastern Conference on Combinatorics, Graph Theory and Computing, Florida, pp. 47–65 (1982)Google Scholar
  6. 6.
    Cheetham, R.P., Oommen, B.J., Ng, D.T.H.: Adaptive structuring of binary search trees using conditional rotations. IEEE Transactions on Knowledge and Data Engineering 5, 695–704 (1993)CrossRefGoogle Scholar
  7. 7.
    Duda, R., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley Interscience, Hoboken (2000)MATHGoogle Scholar
  8. 8.
    Gonnet, G.H., Munro, J.I., Suwanda, H.: Exegesis of self-organizing linear search. SIAM Journal of Comput. 10, 613–637 (1981)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Haykin, S.: Neural Networks and Learning Machines, 3rd edn. Prentice-Hall, Englewood Cliffs (2008)Google Scholar
  10. 10.
    Hester, H.J., Herberger, D.S.: Self-organizing linear search. In: ACM Computing Surveys, pp. 295–311 (1976)Google Scholar
  11. 11.
    Knuth, D.E.: The Art of Computer Programming, vol. 3. Addison-Wesley, Reading (1973)MATHGoogle Scholar
  12. 12.
    Kohonen, T.: Self-Organizing Maps. Springer-Verlag New York, Inc., Secaucus, NJ, USA (1995)CrossRefMATHGoogle Scholar
  13. 13.
    Lai, T.W., Wood, D.: A relationship between self organizing lists and binary search trees. In: Proceedings of the 1991 Int. Conf. Computing and Information, May 1991, pp. 111–116 (1991)Google Scholar
  14. 14.
    Mehlhorn, K.: Data Structures and Algorithms 1: Sorting and Searching. Springer, Berlin (1984)CrossRefMATHGoogle Scholar
  15. 15.
    Oommen, B.J., Hansen, E.R.: List organizing strategies using stochastic move-to-front and stochastic move-to-rear operations. SIAM Journal of Computing 16, 705–716 (1987)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Oommen, B.J., Hansen, E.R., Munro, J.I.: Deterministic optimal and expedient move-to-rear list organizing strategies. Theoretical Computer Science 74, 183–197 (1990)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Oommen, B.J., Ng, D.T.H.: An optimal absorbing list organization strategy with constant memory requirements. Theoretical Computer Science 119, 355–361 (1993)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. Journal of the ACM 32, 652–686 (1985)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Walker, W.A., Gotlieb, C.C.: A top-down algorithm for constructing nearly optimal lexicographical trees. In: Graph Theory and Computing (1972)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • B. John Oommen
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada

Personalised recommendations