Optimal decisions in combining the SOM with nonlinear projection methods

Visual data mining is an efficient way to involve human in search for an optimal decision. This paper focuses on the optimization of the visual presentation of multidimensional data. A variety of methods for projection of multidimensional data on the plane have been developed. At present, a tendency of their joint use is observed. In this paper, two consequent combinations of the self-organizing map (SOM) with two other well-known nonlinear projection methods are examined theoretically and experimentally. These two methods are: Sammon's mapping and multidimensional scaling (MDS). The investigations showed that the combinations (SOM–Sammon and SOM–MDS) have a similar efficiency. This grounds the possibility of application of the MDS with the SOM, because up to now in most researches SOM is applied together with Sammon's mapping. The problems on the quality and accuracy of such combined visualization are discussed. Three criteria of different nature are selected for evaluation of the efficiency of the combined mapping. The joint use of these criteria allows us to choose the best visualization result from some possible ones. Several different initialization ways for nonlinear mapping are examined, and a new one is suggested. A new approach to the SOM visualization is suggested. The obtained results allow us to make better decisions in optimizing the data visualization.