Abstract
In this paper, an original dynamical system derived from dynamic neural fields is studied in the context of the formation of topographic maps. This dynamical system overcomes limitations of the original Self-Organizing Map (SOM) model of Kohonen. Both competition and learning are driven by dynamical systems and performed continuously in time. The equations governing competition are shown to be able to reconsider dynamically their decision through a mechanism rendering the current decision unstable, which allows to avoid the use of a global reset signal.
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References
Alecu, L., Frezza-Buet, H., Alexandre, F.: Can self-organization emerge through dynamic neural fields computation? Connection Science 23(1), 1–31 (2011)
Amari, S.: Dynamics of Pattern Formation in Lateral-Inhibition Type Neural Fields. Biological Cybernetics 27, 77–87 (1977)
Bednar, J.A.: Building a mechanistic model of the development and function of the primary visual cortex. Journal of Physiology-Paris 106(5-6), 194–211 (2012)
Detorakis, G., Rougier, N.: A neural field model of the somatosensory cortex: formation, maintenance and reorganization of ordered topographic maps. PLoS One 7(7), e40257 (2012)
Fix, J.: Python source scripts for generating the illustrations (2013), http://jeremy.fix.free.fr/Simulations/dynamic_som.html (online; accessed November 5, 2013)
Fix, J.: Template based black-box optimization of dynamic neural fields. Neural Networks 46, 40–49 (2013)
Kohonen, T.: Self-organized formation of topologically correct feature maps. Biological Cybernetics 43(1), 59–69 (1982)
Moldakarimov, S.B., McClelland, J.L., Ermentrout, G.B.: A homeostatic rule for inhibitory synapses promotes temporal sharpening and cortical reorganization. Proceedings of the National Academy of Sciences 103(44), 16526–16531 (2006)
Pfeifer, R., Bongard, J.C.: How the Body Shapes the Way We Think: A New View of Intelligence (Bradford Books). The MIT Press (2006)
Turrigiano, G.G.: Homeostatic plasticity in neuronal networks: the more things change, the more they stay the same. Trends in Neurosciences 22(5), 221–227 (1999)
Wilson, H.R., Cowan, J.D.: A Mathematical Theory of the Functional Dynamics of Cortical and Thalamic Nervous Tissue. Kybernetik 13, 55–80 (1973)
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Fix, J. (2014). Dynamic Formation of Self-Organizing Maps. In: Villmann, T., Schleif, FM., Kaden, M., Lange, M. (eds) Advances in Self-Organizing Maps and Learning Vector Quantization. Advances in Intelligent Systems and Computing, vol 295. Springer, Cham. https://doi.org/10.1007/978-3-319-07695-9_2
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DOI: https://doi.org/10.1007/978-3-319-07695-9_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07694-2
Online ISBN: 978-3-319-07695-9
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