Robust Neural Gas for the Analysis of Data with Outliers ∗

Learning the structure of real world data is difficult both to recognize and describe. The structure may contain high dimensional clusters that are related in complex ways. Fur-thermore, real data sets may contain several outliers. Vector quantization techniques has been successfully ap-plied as a data mining tool. In particular the Neural Gas (NG) is a variant of the Self Organizing Map (SOM) where the neighborhoods are adaptively defined during training through the ranking order of the distance of prototypes from the given training sample. Unfortunately, the learning algorithm of the NG is sensi-tive to the presence of outliers as we will show in this paper. Due to the influence of the outliers in the learning process, the topology of the employed network does not conserve the topology of the manifold of the data which is presented. In this paper, we propose to robustify the learning al-gorithm where the parameter estimation process is re-sistant to the presence of outliers in the data. We call this algorithm Robust Neural Gas (RNG). We will illus-trate our technique on synthetic and real data sets