Topological interpolation in SOM by affine transformations.

Abstract

. The calculation of virtual neurons in a self-organizing map by interpolation allows to reduce calculation time and memory space in training and retrieval. In this paper, a new interpolation method, based on affine coordinates of a local system is presented and discussed. An example in the domain of colour mixture is used to show the properties and compare this method to others. 1 Introduction The self-organizing map (SOM) [Koh82] provides a general data approximation method which is suitable for several application domains such as robotics, evaluation of sensory data and visualisation of process states. Recent works [Spe94] have explored the training data distribution and have provided tools for the definition of the number of dimensions of the SOM architecture. It had been shown, that several data sets need higher-dimensional maps for topology preserving mapping. But a serious problem occurs: The number of neurons and consequently the calculation time needed for finding the winner...