Self-organising multilayer topographic mappings

Minimization of distortion measures requires multilayer mappings to be topographic. The author shows this only for tree-like multilayer networks. He also shows how to modify the original topographic mapping learning algorithm to increase its convergence rate. A three-layer network can form linelike feature detectors which are just as good as those in a two-layer network. However, the author finds it necessary to impose explicitly a topological constraint on the learning algorithm to obtain 'perfect' results. This constraint is equivalent to introducing the prior knowledge that the training set of images has the topology of a circle. He has also found that more careful training without this extra topological constraint also yields results of this quality.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>