Visualization of Multidimensional Data Taking into Account the Learning Flow of the Self-Organizing Neural Network

Gintautas Dzemyda, Olga Kurasova
Institute of Mathematics and Informatics
Optimization Department
2600 Vilnius
Lithuania

Keywords: Sammon's mapping, self-organizing maps, neural networks, projection error, visualization.

Abstract

In the paper, we discuss the visualization of multidimensional vectors taking into account the learning flow of the self-organizing neural network. A new algorithm realizing a combination of the self-organizing map (SOM) and Sammon's mapping has been proposed. It takes into account the intermediate learning results of the SOM. The experiments have showed that the algorithm gives lower mean projection errors as compared with a consequent application of the SOM and Sammon's mapping.  This is the essential advantage of the new algorithm, i.e. we succeed to eliminate the influence of the "magic factor" a (0< a £ 1) on Sammon's mapping results. For larger of values of a (a >1), the mean projection error grows. However, in this case the new algorithm operates more stable and gives smaller values of the mean  projection error.