Learning vector quantization without and with habituation

Kohonen's learning vector quantization classifying algorithm is used to classify continuous vectorial inputs into a few categories, divided each from other by some relatively smooth decision boundary. It offers optimal classification in the limit of an infinite number of neurons. In that case a quasi-hydrodynamic treatment is used to explain the sharpness of Bayesian classification for overlapping classes. The opposite limit, namely one neuron per class, is used to illustrate the effect of sensitivity to asymmetry in the geometry of classes. A procedure called habituation reduces the asymmetry and thereby the classification error.<>