Magnification Control in Neural Maps

Neural maps can be taken as biologically inspired vector quantizers including the concept of neighborhood cooperativeness in standard vector quantization. Two important models are self-organizing maps (SOM) and neural gas (NG). Besides the standard error, the squared reconstruction error, several other parameters exist to assess the properties of a map. One of these is the so-called magnification of a map which relates the data probability density to the weight vector density achieved after learning. In the talk we consider different ways to control the magnification in SOM and NG. Starting from well-known and extended control approaches for SOM we transfer these ideas to the NG. We show that the approaches are similar but not identic. Moreover we emphasize the fact that the NG results are valid for any data dimension whereas in the SOM case the results only hold for the one-dimensional case.

B.Hammer