Self-Organizing Feature Maps with Self-Organizing Neighborhood Widths
Michael Herrmann · 2005
Self-organizing feature maps with self-determined local neighborhood widths are applied to construct principal manifolds of data distributions. This task exemplifies the problem of the learning of learning parameters in neural networks. The proposed algorithm is based upon analytical results on phase transitions in self-organizing feature maps available for idealized situations. By illustrative simulations it is demonstrated that deviations from the theoretically studied situation are compensated adaptively and that the capability of topology preservation is crucial for avoiding overfitting effects. Further, the relevance of the parameter learning scheme for hierarchical feature maps is stated. 1 Introduction Many learning algorithms are influenced by the choice and by the course of on-line modification of particular parameters. Whereas the learning algorithm itself represents a formalized principle such as the minimization of an error measure, principles to govern parameter settings ...