find dependences between self organizing maps (general Question)

I have a multi-dimensional set of data, where a dependent variable depends on many parameters of my data set. With self-organizing-maps you can build maps and see strong and weak dependences between the values just by comparing the colorful patterns of the maps. If one parameter has great influence on my dependent variable, you can see such primary dependences immediately when the patterns are equal.

I now search a method to blank out these primary dependences and try to extract the secondary dependences. How to make visible the influence of other parameters on my dependent variable? Any Ideas? To make clear what is a self-organizing map, I show you this picture as an example (from the Internet). It's not my set of data !