In the marginally stable ordered state of Kohonen's feature-map neural-network model the distribution of fluctuating distances between neighboring cells is found to be a self-similar Weierstrass-Mandelbrot-type function with a nontrivial scaling exponent. The relationship among the quantities describing the distribution is discussed in terms of a balance between a deterministic multiplicative and a stochastic additive process, described by a Perron-Frobenius operator. Two regions of the Kohonen learning parameter α, separated by αc0.63, differ in the character of both fluctuation and ordering, the latter being fastest close to αc.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics