Luttrell S P, August 1992, Code vector density in topographic mappings, DRA technical report (Malvern, UK), 4669
In this memorandum we present an informally argued derivation of the properties of topographic vector quantisers in the limit of a large codebook size. In particular, we prove that the code vector density does not depend on one's choice of neighbourhood function, provided that we use the minimum distortion (rather than the nearest neighbour) encoding prescription. This result suggests that widespread use of the nearest neighbour prescription in topographic mapping networks is fundamentally misguided. It would be advisable to remember that the nearest neighbour prescription is assumed not derived, so its adherents must accept defeat gracefully.