In this paper we propose a novel class of learning vector quantizers (LVQ) based on multivariate data ordering. Linear LVQ is not the optimal estimator for non-Gaussian multivariate data distributions. Furthermore, it is not robust either in the case of outliers or in the case of erroneous decisions. The novel LVQs use multivariate ordering in order to obtain location estimators that are robust and that provide superior and, in certain cases, optimal performance for non-Gaussian multivariate distributions. A special case of the novel LVQ class is the marginal median LVQ (MM LVQ), which uses the marginal median as multivariate estimator of location.