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Topological feature maps with self-organized lateral connections: a population-coded, one-layer model of associative memory

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Abstract

Guided by the neurobiological principles of self-organization and population coding, we develop a simple, neural, one-layer model for auto-association. Its core is a feature map endowed with self-organized lateral connections. Input patterns are coded by small spots of active neurons. The time evolution of neural activity then realizes an auto-association process by a recurrent attractor dynamics. Population coding is preserved due to a balance of diffusive spreading of activity and competitive refocusing. Because of its simplicity, the model allows a thorough qualitative and quantitative understanding. We show that the network is capable of performing a cluster analysis and hierarchical classification of data and, thus, qualifies as a tool for unsupervised statistical data analysis.

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References

  • Abramowitz M, Stegun IA (eds) (1984) Handbook of mathematical functions. Harry Deutsch Verlag, Thun

    Google Scholar 

  • Adolphs U (1992) Selbstorganisierende Perzeptronstrukturen mit radialen Basisfunktionen. Diplomarbeit Physik-Department, Technische Universität München

  • Baldi P, Heiligenberg W (1988) How sensory maps could enhance resolution through ordered arrangements of broadly tune receivers. Biol Cybern 59:313–318

    Google Scholar 

  • Cooper L (1974) A possible organization of animal memory and learning. In: Lundquist B, Lindquist S (eds) Proc Nobel Symp Collective Properties of Physical Systems. Acad Press, New York

    Google Scholar 

  • Dersch DR, Tavan P (1994) Asymptotic level density in topological feature maps. IEEE Trans Neural Net, in press

  • Duda RO, Hart PE (1973) Pattern classification and scene analysis. Wiley, New York

    Google Scholar 

  • Gardiner CW (1990) Handbook of stochastic methods. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Haken H (1983) Synergetics. An introduction. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Hemmen JL van, Joffe L, Kühn R, Vaas M (1990) Increasing the efficiency of a neural network through unlearning. Physica 163A: 386–392

    Google Scholar 

  • Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79:2554–2558

    Google Scholar 

  • Hopfield JJ, Feinstein DI, Palmer RG (1983) ‘Unlearning’ has a stabilizing effect on collective memories. Nature 304:158–159

    Google Scholar 

  • Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69

    Google Scholar 

  • Kosko B (1988) Bidirectional associative memories. IEEE Trans Syst Man Cybern 18:49–60

    Google Scholar 

  • Kunstmann N, Hillermeier C, Rabus B, Tavan P (1994) An associative memory that can form hypotheses—a phase-coded neural network. Biol Cybern, in press

  • Kunstmann N, Hillermeier C, Tavan P (1993) Associative memories that can form hypotheses: phased-coded network architectures. Proc ICANN, Amsterdam

  • Linde Y, Buzo A, Gray RM (1980) An algorithm for vector quantizer design. IEEE Trans Comm 28:84–95

    Google Scholar 

  • Malsburg C von der (1981) The correlation theory of brain function. (Technical Report 81–2) Department für Neurobiologie, MaxPlanck-Institut für Biophysikalische Chemie, Göttingen

    Google Scholar 

  • Moody J, Darken C (1989) Fast learning in networks of locally-tuned processing units. Neural Comput 1:281–294

    Google Scholar 

  • Poggio T, Girosi F (1990) Regularization algorithms for learning that are equivalent to multilayer networks. Science 247: 978–982

    Google Scholar 

  • Rabus B (1992) Hypothesenbildung in phasenkodierten Assoziativspeichern. Diplomarbeit Physik-Department, Technische Universität München

  • Reichl LE (1980) A modern course in statistical physics. University of Texas Press, Austin.

    Google Scholar 

  • Ritter H (1991) Asymptotic level density for a class of vector quantization processes. IEEE Trans Neural Net 1:173–175

    Google Scholar 

  • Sparks D, Lee C, Rohrer W (1990) Population coding of the direction, amplitude, and velocity of saccadic eye-movements in the superior colliculus. Cold Spring Harbor Symp Quant Biol 55:805–811

    Google Scholar 

  • Tavan P, Grubmüller H, Kühnel H (1990) Self-organization of associative memory and pattern classification: recurrent signal processing on topological feature maps. Biol Cybern 64:95–105

    Google Scholar 

  • Willshaw DJ, Malsburg C von der (1976) How patterned neural connections can be set up by self-organization. Proc R Soc Lond [Biol] 194:431–445

    Google Scholar 

  • Zador PL (1982) Asymptotic quantization error of continuous signals and the quantization dimension. IEEE Trans Inform Theor 28:139–149

    Google Scholar 

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Hillermeier, C., Kunstmann, N., Rabus, B. et al. Topological feature maps with self-organized lateral connections: a population-coded, one-layer model of associative memory. Biol. Cybern. 72, 103–117 (1994). https://doi.org/10.1007/BF00205975

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  • DOI: https://doi.org/10.1007/BF00205975

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