Using self-organizing maps for regression: the importance of the output function

Self-organizing map (SOM) is a powerful paradigm that is extensively applied for clustering and visualization purpose. It is also used for regression learning, especially in robotics, thanks to its ability to provide a topological projection of high dimensional non linear data. In this case, data extracted from the SOM are usually restricted to the best matching unit (BMU), which is the usual way to use SOM for classification, where class labels are attached to individual neurons. In this article, we investigate the influence of considering more information from the SOM than just the BMU when performing regression. For this purpose, we quantitatively study several output functions for the SOM, when using these data as input of a linear regression, and find that the use of additional activities to the BMU can strongly improve regression performance. Thus, we propose an unified and generic framework that embraces a large spectrum of models from the traditional way to use SOM, with the best matching unit as output, to models related to the radial basis function network paradigm, when using local receptive field as output.