A note on the sensitivity to parameters in the convergence of Self-Organizing Maps

This paper is aimed to study what are the parameters having the largest influence on the convergence of Kohonen Self Organizing Maps (SOMs), with particular attention to the occurrence of meta–stable states when systems of maps are employed. The underlying assumption is that, notwithstanding the random initialization of the SOMs and randomization of patterns presentation, trained maps configurations should converge to an ‘optimal’ mapping of the original data–set. Therefore, we should look for a set of learning parameters that minimizes the divergence between SOMs that are trained from the same input space. To such purpose we will introduce a Convergence Index, which is able to test the robustness of the fit of trained SOMs to their input space. Such arguments will be tested with a highly non linear financial data–set, and some conclusions will be drawn about the architecture which is best suited to generate robust Kohonen Maps.