Luttrell S P, May 1990, Asymptotic code vector density in topographic vector quantisers, RSRE technical report (Malvern, UK), 4392
In this memorandum we use a noise-robust vector quantiser model to derive expressions for the asymptotic code vector density \[Rho] in various types of topographic vector quantisers. A topographic vector quantiser is not identical to a standard (i.e. Kohonen) topographic mapping, but the differences are minimal, In all the cases that we study (scalar and vector quantisation with various symmetric topographic neighbourhoods) we obtain the asymptotic result \[Rho] \[Proportional] P^(N/(N+2)), where N is the input dimensionality and P is the input probability density. Thus the asymptotic code vector densities of a topographic vector quantiser and a standard vector quantiser are the same.