Skip to main content
Log in

Using an Hebbian Learning Rule for Multi-Class SVM Classifiers

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

Regarding biological visual classification, recent series of experiments have enlighten the fact that data classification can be realized in the human visual cortex with latencies of about 100–150 ms, which, considering the visual pathways latencies, is only compatible with a very specific processing architecture, described by models from Thorpe et al.

Surprisingly enough, this experimental evidence is in coherence with algorithms derived from the statistical learning theory. More precisely, there is a double link: on one hand, the so-called Vapnik theory offers tools to evaluate and analyze the biological model performances and on the other hand, this model is an interesting front-end for algorithms derived from the Vapnik theory.

The present contribution develops this idea, introducing a model derived from the statistical learning theory and using the biological model of Thorpe et al. We experiment its performances using a restrained sign language recognition experiment.

This paper intends to be read by biologist as well as statistician, as a consequence basic material in both fields have been reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bajcsy R, Solina F (1987) Three dimensional object representa-tion revisited. In: Proceedings of the 1st International Conference on Computer Vision. London, England, IEEE Computer Society Press.

    Google Scholar 

  • Bartlett P, Shawe-Taylor J (1999) Generalization performance of sup-port vector machines and other pattern classifiers. In: B Schölkopf, C Burges, A Smola, eds. Advances in Kernel Methods, Support Vector Learning. The MIT Press, Cambridge, Chapt. 4, pp. 43–54.

    Google Scholar 

  • Baum E, Haussler D (1989) What size net gives valid generalization. Neural Comput. 1: 151–160.

    Google Scholar 

  • Benedetti R, Risler J-J (1990) Real Algebraic and Semi-Algebraic Sets. Hermann, Paris.

    Google Scholar 

  • Bugmann G (1997) Biologically plausible neural computation. Biosystems 40: 11–19.

    Google Scholar 

  • Bullier J (2001) Integrated model of visual processing. Brain Res. Reviews 36: 96–107.

    Google Scholar 

  • Burnod Y(1993) An Adaptive Neural Network: The Cerebral Cortex, 2nd edition. Masson, Paris.

    Google Scholar 

  • Carr CE (1993) Processing of temporal information in the brain. Annu. Rev. Neurosci. 16: 223–244.

    Google Scholar 

  • Chang C-C, Lin C-J (2001) Training nu-support vector classi-fiers: Theory and algorithms. Neural Comput. 13(9): 2119–214.

    Google Scholar 

  • Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans. on Information Theory 13(1).

  • Delorme A, Gautrais J, Van Rullen R, Thorpe SJ (1999) SpikeNET: A simulator for modeling large networks of integrate and fire neurons. Neurocomput. 26: 989–996.

    Google Scholar 

  • Delorme A, Richard G, Fabre-Thorpe M(2000) Rapid categorisation of natural scenes is colour blind: A study in monkeys and humans. Vision Research 40(16): 2187–2200.

    Google Scholar 

  • Delorme A, Thorpe S (2001) Face processing using one spike per neuron: Resistance to image degradation. Neural Networks 14: 795–804.

    Google Scholar 

  • Duda RO, Hart PE, Stork DG (2000) Pattern Classification, 2nd edition. Wiley Interscience.

  • Durbin R, Miall C, Mitchinson G, eds. (1989) The Computing Neuron. Addison-Wesley.

  • Figueiredo MAT, Jain AK (2001) Bayesian learning of sparse classifiers. In: Computer Vision and Pattern Recognition.

  • Freedman DJ, Riesenhuber M, Poggio T, Miller EK (2002) Cate-gorical representation of visual stimuli in the primate prefrontal cortex. Science 291(5502): 312–316.

    Google Scholar 

  • Friess T, Cristianini N, Campbell C (1998) The kernel adatron al-gorithm: A fast and simple learning procedure for support vec-tor machine. In: Proc. 15th International Conference on Machine Learning. Morgan Kaufman.

  • Gaspard F, Viéville T (2000) Non linear minimization and visual localization of a plane. In: The 6th International Conference on Information Systems, Analysis and Synthesis, Vol. VIII, pp. 366–371.

    Google Scholar 

  • Gautrais J, Thorpe S (1998) Rate coding vs temporal order coding: A theorical approach. Biosystems 48: 57–65.

    Google Scholar 

  • Gisiger T, Dehaene S, Changeux JP (2000) Computational models of association cortex. Curr. Opin. Neurobiol. 10: 250–259.

    Google Scholar 

  • Guermeur Y (2002a) Combining discriminant models with new multi-class SVMs. Pattern Analysis and Applications 5(2): 168–179.

    Google Scholar 

  • Guermeur Y(2002b) Asimple unifying theory of multi-class support vector machines. Technical Report 4669, INRIA.

  • Gutierrez-Galvez A, Gutierrez-Osuna R (2003) Pattern completion through phase coding in population neurodynamics. Neural Networks 16: 649–656.

    Google Scholar 

  • Hubel D (1994) L'oeil, le Cerveau et la Vision: Les étapes cérébrales du traitement visuel, L'univers des sciences. Pour la science.

  • Huerta R, Nowotn T, García-Sanchez M, Abarbanel HDI, Rabinovich MI (2004) Learning classification in the olfactory system of insects. In preparation.

  • Koiran P, Sontag E (1996) Neural networks with quadratic VC dimension.

  • Advances in Neural Information Processing System 8: 197–203.

  • Krauth W, Mezard M (1987) Learning algorithms with optimal stability in neural networks. J. Phis. 20}: 745–752.

    Google Scholar 

  • Marr D (1982) Vision. W.H. Freeman and Co.

  • Mezard M, Nadal J (1989) Learning in feed forward layered net-works: The tiling algorithm. J. Phys. 22: 2191–2204.

    Google Scholar 

  • Novak L, Bullier J (1997) The Timing of Information Transfer in the Visual System, Vol. 12 of Cerebral Cortex, Chap. 5, pp. 205–241. Plenum Press, New York.

    Google Scholar 

  • Rolls ET, Treves A (1998) Neural Networks and Brain Function. Oxford University Press.

  • Shawe-Taylor J, Bartlett P, Williamson R, Anthony M (1998) Structural risk minimization over data-dependent hierarchies. IEEE Trans. on Information Theory 44(5).

  • Soo-Young L, Dong-Gyu J (1996) Merging back-propagation and Hebbian learning rules for robust classifications. Neural Networks 9(7): 1213–1222.

    Google Scholar 

  • Theodoridis S, Koutroumbas K (1999) Pattern Recognition. Academic Press.

  • Thorpe S (2002) Ultra-rapid scene categorization with a wave of spikes. In: Biologically Motivated Computer Vision, Vol. 2525 of Lecture Notes in Computer Science. Springer-Verlag Heidelberg, pp. 1–15.

    Google Scholar 

  • Thorpe S, Delorme A, Van Rullen R (2001) Spike based strategies for rapid processing. Neural Networks 14: 715–726.

    Google Scholar 

  • Thorpe S, Fabre-Thorpe M (2001) Seeking categories in the brain. Science 291: 260–263.

    Google Scholar 

  • Thorpe S, Fize D, Marlot C (1996) Speed of processing in the human visual system. Nature 381: 520–522.

    Google Scholar 

  • van Tonder GJ, Ejima Y (2000) Bottom-up clues in target finding: Why a Dalmatian may be mistaken for an elephant. Perception 29(2): 149–157.

    Google Scholar 

  • Vapnik V(1995) The Nature of Statistical Learning Theory. Springer-Verlag.

  • Vapnik V (1998) Statistical Learning Theory. John Wiley.

  • Vieville T (2000) Using markers to compensate displacements in MRI volume sequences. Technical Report 4054, INRIA.

  • Vieville T, Lingrand D, Gaspard F (2001) Implementing a multi-model estimation method. The International Journal of Computer Vision 44(1).

  • Wilson R, Keil F (1999) The MIT Encyclopedia of the Cognitive Sciences. MIT Press, Cambridge, MA.

    Google Scholar 

  • Yu AJ, Giese M, Poggio T (2003) Biophysiologically plausi-ble implementations of maximum operation. Neural Comput. 14(12).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Viéville, T., Crahay, S. Using an Hebbian Learning Rule for Multi-Class SVM Classifiers. J Comput Neurosci 17, 271–287 (2004). https://doi.org/10.1023/B:JCNS.0000044873.20850.9c

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JCNS.0000044873.20850.9c

Navigation