Local linear correlation analysis with the SOM

The purpose of this paper is to illustrate a method which can be used to select relevant input variables for non-linear regression. The proposed method is an extension to the concept of SOM such that the linear correlation coefficient is computed over a whole data manifold in neighbour subspaces. Using the topographic properties of the usual SOM a localised correlation coefficient may be obtained by modified Kohonen learning. The graphical ordered plot of the obtained local correlation allows to study the non-linear dependencies of variables