Magnification control in neural maps.
Thomas Villmann, J. Michael Herrmann · Edinburgh Research Explorer (University of Edinburgh) · 1998
In self-organising maps reconstruction error minimization and topology preservation have shown to be conflicting goals. For one dimensional maps this dilemma can be alleviated e.g. by locally adaptive learning rates. On the other hand, the neural gas algorithm and its topology representing extension allow for vector quantization at theoretically optimal reconstruction error for arbitrary data dimensionality . Thus, it is possible to modify the neural gas algorithm such as to meet optimality criteria other than mean square error in an exact way for data dimensions greater than one.