SOM-based similarity index measure: quantifying interactions between multivariate structures

This paper addresses the issue of quantifying asymmetric functional relationships between signals. We specifically consider a previously proposed similarity index that is conceptually powerful, yet computationally very expensive. The complexity increases with the square of the number of samples in the signals. In order to counter this difficulty, a self-organizing map that is trained to model the statistical distribution of the signals of interest is introduced in the similarity index evaluation procedure. The SOM based technique is equally accurate, but computationally less expensive compared to the conventional measure. These results are demonstrated by comparing the original and SOM-based similarity index approaches on synthetic chaotic signal and real EEG signal mixtures.