Heuristic approach for minimizing the projection error in the integrated mapping

In this paper, we have developed and examined a heuristic approach for minimizing the projection error in Sammon's mapping applied in combination with the self-organizing map (SOM). As a final result, we need to visualize the neurons-winners of the SOM. The criterion of visualization quality is the projection error of Sammon's mapping. Two combinations were considered: (1) a consecutive application of the SOM and Sammon's mapping and (2) Sammon's mapping taking into account the learning flow of the self-organizing neural network (integrated combination of the mapping methods). The goal is to obtain a lower projection error and its lower dependence on the so-called ‘magic factor’ in Sammon's mapping. Different modifications of Sammon's mapping are examined experimentally and applied in the combination with the SOM. A parallel algorithm of the integrated combination has been proposed.