Relations between generalized fractal dimensions and Kohonen's self-organizing map

In this paper we present a method to improve the learning results for diierent data sets, which earlier were diicult or impossible to learn, and to criticize the map's development during learning. Calculating the generalized fractal dimensions of the data set we choose the map's dimension accordingly for guaranteeing the maps ability of topology preservation. Furthermore we explore diierent states of the learning process and the nal map for its fractal dimensions and are able to measure the map's development in the training phase. Keywords Self-organizing map, generalized fractal dimensions, measuring the input data's extensions in hyperspace, nding the principal manifolds of the input data, waber product, topology preservation 1 Introduction