Convergence properties of Kohonen's topology conserving maps: fluctuations, stability, and dimension selection
Biological CyberneticsPublished 1 November 1988
Helge Ritter, Klaus Schulten
Citations325
SJR quartileQ2
SJR score0.52
SNIP0.78
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TL;DR
A Markovian algorithm for the formation of topologically correct feature maps proposed earlier by Kohonen is analysed and an instability responsible for a phenomenon termed by Koh Finnish “automatic selection of feature dimensions” is studied.
Abstract
We analyse a Markovian algorithm for the formation of topologically correct feature maps proposed earlier by Kohonen. The maps from a space of input signals onto an array of formal neurons are generated by a learning scheme driven by a random sequence of input samples. The learning is described by an equivalent Fokker-Planck equation. Convergence to an equilibrium map can be ensured by a criterion for the time dependence of the learning step size. We investigate the stability of the equilibrium map and calculate the fluctuations around it. We also study an instability responsible for a phenomenon termed by Kohonen “automatic selection of feature dimensions”.
Keywords
Computer ScienceNeuroscience
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