Robust self-organization with M-estimators

•A new self-organizing map model is presented, which is based on M-estimators.•The new model features scale invariance, unlike previous approaches.•Our model outperforms its competitors in data visualization and color quantization applications.•The particular M-estimator to use depends on the problem at hand.

Most of the work done on self-organizing maps relies on the minimization of the mean squared error. This nonrobust approach leads to poor performance in the presence of outliers. Here we consider robust M-estimators as an alternative for least squares in the context of self-organization. New learning rules are derived, so that the original Kohonen׳s SOFM learning rule is a particular case. Experimental results are presented which demonstrate the robustness of our method against outliers, when compared to other robust self-organizing maps.