Neurons, Dendrites, and Pattern Classification

  • Gerhard X. Ritter
  • Laurentiu Iancu
  • Gonzalo Urcid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2905)


Computation in a neuron of a traditional neural network is accomplished by summing the products of neural values and connection weights of all the neurons in the network connected to it. The new state of the neuron is then obtained by an activation function which sets the state to either zero or one, depending on the computed value. We provide an alternative way of computation in an artificial neuron based on lattice algebra and dendritic computation. The neurons of the proposed model bear a close resemblance to the morphology of biological neurons and mimic some of their behavior. The computational and pattern recognition capabilities of this model are explored by means of illustrative examples and detailed discussion.


Hide Layer Training Algorithm Output Neuron Radial Basis Function Neural Network Pattern Classification 
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.


  1. 1.
    Eccles, J.C.: The Understanding of the Brain. McGraw-Hill, New York (1977)Google Scholar
  2. 2.
    Koch, C., Segev, I. (eds.): Methods in Neuronal Modeling: From Synapses to Networks. MIT Press, Boston (1989)Google Scholar
  3. 3.
    Segev, I.: Dendritic Processing. In: Arbib, M. (ed.) The Handbook of Brain Theory and Neural Networks, pp. 282–289. MIT Press, Boston (1998)Google Scholar
  4. 4.
    Arbib, M.A. (ed.): The Handbook of Brain Theory and Neural Networks. MIT Press, Boston (1998)Google Scholar
  5. 5.
    Holmes, W.R., Rall, W.: Electronic Models of Neuron Dendrites and Single Neuron Computation. In: McKenna, T., Davis, J., Zornetzer, S.F. (eds.) Single Neuron Computation, pp. 7–25. Academic Press, San Diego (1992)Google Scholar
  6. 6.
    McKenna, T., Davis, J., Zornetzer, S.F. (eds.): Single Neuron Computation. Academic Press, San Diego (1992)zbMATHGoogle Scholar
  7. 7.
    Mel, B.W.: Synaptic Integration in Excitable Dendritic Trees. J. of Neurophysiology 70, 1086–1101 (1993)Google Scholar
  8. 8.
    Rall, W., Segev, I.: Functional Possibilities for Synapses on Dendrites and Dendritic Spines. In: Edelman, G.M., Gall, E.E., Cowan, W.M. (eds.) Synaptic Function, pp. 605–636. Wiley, New York (1987)Google Scholar
  9. 9.
    Shepherd, G.M.: Canonical Neurons and their Computational Organization. In: McKenna, T., Davis, J., Zornetzer, S.F. (eds.) Single Neuron Computation, pp. 27–55. Academic Press, San Diego (1992)Google Scholar
  10. 10.
    Gori, M., Scarselli, F.: Are Multilayer Perceptrons Adequate for Pattern Recognition and Verification? IEEE Trans. on Pattern Analysis and Machine Intelligence 20(11), 1121–1132 (1998)CrossRefGoogle Scholar
  11. 11.
    Davidson, J.L.: Simulated Annealing and Morphological Neural Networks. In: Image Algebra and Morphological Image Processing III. Proc. SPIE 1769, San Diego, CA, July 1992, pp. 119–127 (1992)Google Scholar
  12. 12.
    Davidson, J.L., Hummer, F.: Morphology Neural Networks: An Introduction with Applications. IEEE Systems and Signal Processing 12(2), 177–210 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Davidson, J.L., Srivastava, R.: Fuzzy Image Algebra Neural Network for Template Identification. In: Second Annual Midwest Electro-Technology Conference, Ames, IA, April 1993, pp. 68–71 (1993)Google Scholar
  14. 14.
    Davidson, J.L., Talukder, A.: Template Identification Using Simulated Annealing in Morphology Neural Networks. In: Second Annual Midwest Electro-Technology Conference, Ames, IA, April 1993, pp. 64–67 (1993)Google Scholar
  15. 15.
    Ritter, G.X., Sussner, P.: Associative Memories Based on Lattice Algebra. In: IEEE Inter. Conf. Systems, Man, and Cybernetics, Orlando, FL, October 1997, pp. 3570–3575 (1997)Google Scholar
  16. 16.
    Ritter, G.X., Sussner, P., Diaz de Leon, J.L.: Morphological Associative Memories. IEEE Trans. on Neural Networks 9(2), 281–293 (1998)CrossRefGoogle Scholar
  17. 17.
    Ritter, G.X., Diaz de Leon, J.L., Sussner, P.: Morphological Bidirectional Associative Memories. Neural Networks 12, 851–867 (1999)CrossRefGoogle Scholar
  18. 18.
    Ritter, G.X., Urcid, G., Iancu, L.: Reconstruction of Noisy Patterns Using Morphological Associative Memories. J. of Mathematical Imaging and Vision 19(5), 95–111 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Suarez-Araujo, C.P., Ritter, G.X.: Morphological Neural Networks and Image Algebra in Artificial Perception Systems. In: Image Algebra and Morphological Image Processing III. Proc. SPIE 1769, San Diego, CA, July 1992, pp. 128–142 (1992)Google Scholar
  20. 20.
    Sussner, P.: Observations on Morphological Associative Memories and the Kernel Method. Neurocomputing 31, 167–183 (2000)CrossRefGoogle Scholar
  21. 21.
    Won, Y., Gader, P.D.: Morphological Shared Weight Neural Network for Pattern Classification and Automatic Target Detection. In: Proc. 1995 IEEE International Conference on Neural Networks, Perth, Western Australia (November 1995)Google Scholar
  22. 22.
    Won, Y., Gader, P.D., Coffield, P.: Morphological Shared-Weight Networks with Applications to Automatic Target Recognition. IEEE Trans. on Neural Networks 8(5), 1195–1203 (1997)CrossRefGoogle Scholar
  23. 23.
    Ritter, G.X., Urcid, G.: Lattice Algebra Approach to Single Neuron Computation. IEEE Trans. on Neural Networks 14(2), 282–295 (2003)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Ritter, G.X., Iancu, L.: Morphological Perceptrons. Preprint submitted to IEEE Trans. on Neural NetworksGoogle Scholar
  25. 25.
    Lang, K.J., Witbrock, M.J.: Learning to Tell Two Spirals Apart. In: Touretzky, D., Hinton, G., Sejnowski, T. (eds.) Proc. of the 1988 Connectionist Model Summer School, pp. 52–59. Morgan Kaufmann, San Mateo (1988)Google Scholar
  26. 26.
    Wasnikar, V.A., Kulkarni, A.D.: Data Mining with Radial Basis Functions. In: Dagli, C.H., et al. (eds.) Intelligent Engineering Systems Through Artificial Neural Networks, ASME Press, New York (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Gerhard X. Ritter
    • 1
  • Laurentiu Iancu
    • 1
  • Gonzalo Urcid
    • 2
  1. 1.CISE Dept.University of FloridaGainesvilleUSA
  2. 2.Optics Dept.INAOETonantzintlaMexico

Personalised recommendations