Abstract
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.
Chapter PDF
Similar content being viewed by others
Keywords
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
Eccles, J.C.: The Understanding of the Brain. McGraw-Hill, New York (1977)
Koch, C., Segev, I. (eds.): Methods in Neuronal Modeling: From Synapses to Networks. MIT Press, Boston (1989)
Segev, I.: Dendritic Processing. In: Arbib, M. (ed.) The Handbook of Brain Theory and Neural Networks, pp. 282–289. MIT Press, Boston (1998)
Arbib, M.A. (ed.): The Handbook of Brain Theory and Neural Networks. MIT Press, Boston (1998)
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)
McKenna, T., Davis, J., Zornetzer, S.F. (eds.): Single Neuron Computation. Academic Press, San Diego (1992)
Mel, B.W.: Synaptic Integration in Excitable Dendritic Trees. J. of Neurophysiology 70, 1086–1101 (1993)
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)
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)
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)
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)
Davidson, J.L., Hummer, F.: Morphology Neural Networks: An Introduction with Applications. IEEE Systems and Signal Processing 12(2), 177–210 (1993)
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)
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)
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)
Ritter, G.X., Sussner, P., Diaz de Leon, J.L.: Morphological Associative Memories. IEEE Trans. on Neural Networks 9(2), 281–293 (1998)
Ritter, G.X., Diaz de Leon, J.L., Sussner, P.: Morphological Bidirectional Associative Memories. Neural Networks 12, 851–867 (1999)
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)
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)
Sussner, P.: Observations on Morphological Associative Memories and the Kernel Method. Neurocomputing 31, 167–183 (2000)
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)
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)
Ritter, G.X., Urcid, G.: Lattice Algebra Approach to Single Neuron Computation. IEEE Trans. on Neural Networks 14(2), 282–295 (2003)
Ritter, G.X., Iancu, L.: Morphological Perceptrons. Preprint submitted to IEEE Trans. on Neural Networks
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ritter, G.X., Iancu, L., Urcid, G. (2003). Neurons, Dendrites, and Pattern Classification. In: Sanfeliu, A., Ruiz-Shulcloper, J. (eds) Progress in Pattern Recognition, Speech and Image Analysis. CIARP 2003. Lecture Notes in Computer Science, vol 2905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24586-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-24586-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20590-6
Online ISBN: 978-3-540-24586-5
eBook Packages: Springer Book Archive
