Supervised Kohonen networks for classification problems

In this paper the transparency of the Counter Propagation Network (CPN) and the modelling power of the supervised Kohonen network (SKN) is combined. Two alternative supervised Kohonen networks are introduced: the AY-fused (XYF) and the Bi-Directional Kohonen (BDK) network. Both networks have in common that they deal in a straightforward and concise way with the (non-linear) relationship between the topology of the data and the corresponding class membership. The XYF network exploits a weighted and normalised similarity between a data object and the units in the input and output maps for the simultaneous update of the network maps, whereas the BDK network uses this weighted similarity measure to update the input and output map in an alternating way. It will be shown that both XYF and BDK networks yield better prediction models (expressed by the overall model accuracy) than the classical CPN and SKN networks. This study focuses solely on multi-output classification problems. Because in supervised self-organising maps (binary) class information is combined with continuous input values, we investigated the influence of two similarity measures applied to the output maps: the Euclidean and the Tanimoto distance. It will be shown that the Tanimoto distance measure yields better results. Two additional learning mechanisms will be introduced: adaptive learning and dynamical weight decay. Adaptive learning can improve network performance for difficult data sets. Inclusion of dynamical weight decay does this, too, and is especially useful for XYF and BDK networks. Various ways to analyse the maps of the supervised Kohonen networks are introduced in this paper as well. For example, the average input profiles for each particular class membership and the visualisation of the correlation coefficients computed for all unit weights in the input and output map serve as additional tools to analyse the content of the networks and the nature of the relationship between the input and the output objects. (c) 2006 Elsevier B.V All rights reserved.