Certain facts about Kohonen's LVQ1 algorithm

Vector Quantizers are structurally well suited to perform the classification task, provided that codebook vectors are labeled. In order to achieve a satisfactory performance/complexity ratio, the position of labeled codebook vectors should be adapted in the feature space. A class of such adaptive algorithms, called LVQ, was proposed by Kohonen in the framework of Neural Networks. In this brief we present a study about the first algorithm of this class, called LVQl. As a main contribution, we provide the analytical form for the criterion underlying LVQ1.