Optimal decisions in combining the SOM with nonlinear projection methods Jolita Bernatavic ˇien _ e, Gintautas Dzemyda, Olga Kurasova, Virginijus Marcinkevic ˇius * Institute of Mathematics and Informatics, Akademijos St. 4, 08663 Vilnius, Lithuania Received 5 November 2004; accepted 24 May 2005 Available online 6 December 2005 Abstract Visual data mining is an efficient way to involve human in search for a 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 ten- dency 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: SammonÕs 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 SammonÕs mapping. The problems on the quality and accuracy of such combined visualization are discussed. Three criteria of different nature are selected for evaluation the efficiency of the combined mapping. The joint use of these criteria allows us to choose the best visual- ization 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. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Neural networks; Visual interactive modelling; Optimization; SOM; Visual data mining 0377-2217/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.05.030 * Corresponding author. E-mail addresses: JolitaB@ktl.mii.lt (J. Bernatavic ˇien _ e), Dzemyda@ktl.mii.lt (G. Dzemyda), Kurasova@ktl.mii.lt (O. Kurasova), VirgisM@ktl.mii.lt (V. Marcinkevic ˇius). European Journal of Operational Research 173 (2006) 729–745 www.elsevier.com/locate/ejor