A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

Keywords: Topology preserving Self-organizing map Growing cell structures Visualization methods Delaunay triangulation The Self-Organizing Map (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topology preservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topology preservation, particularly using Kohonen's model. In this work, two methods for measuring the topology preservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving map.