Forbidden Magnification? I

This paper presents some interesting results obtained by the algorithm by Bauer, Der and Hermann (BDH) [1] for magnification control in Self-Organizing Maps. Magnification control in SOMs refers to the modification of the relationship between the probability density functions of the input samples and their prototypes (SOM weights). The above mentioned algorithm enables explicit control of the magnification properties of a SOM, however, the available theory restricts its validity to 1-D data or 2-D data when the stimulus density separates. This discourages the use of the BDH algorithm for practical applications. In this paper we present results of careful simulations that show the scope of this algorithm when applied to more general, ”forbidden” data. We also demonstrate the application of negative magnification to magnify rare classes in the data to enhance their detectability.