  We consider a generalization of the criterion minimized by the K-means
algorithm, where a neighborhood structure is used in the calculus of the
variance. Such tool is used, for example with Kohonen maps, to measure the
quality of the quantification preserving the neighborhood relationships. If we
assume that the parameter vector is in a compact Euclidean space and all it
components are separated by a minimal distance, we show the strong consistency
of the set of parameters almost realizing the minimum of the empirical extended
variance.
