Self-Organizing Feature Maps with Self-Organizing Neighborhood Widths

Self-organizing feature maps with self-determined local neighborhood widths are applied to construct principal manifolds of data distributions. This task exempli es 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 over tting e ects. Further, the relevance of the parameter learning scheme for hierarchical feature maps is stated.