Consistance d'un estimateur de minimum de variance étendue

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 a 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 its 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. To cite this article: J. Rynkiewicz, C. R. Acad. Sci. Paris, Ser. I 341 (2005).