A new quantitative measure of topology preservation in Kohonen´s feature maps

In this paper we give a new approach for quantifying topology preservation using explicitly the structure of the data manifold. It can be applied to linear and nonlinear data manifolds M. Further, this method allows one to quantify the range of folds. Our approach employs what we call the topographic function, which is defined based on the so called masked Voronoi polyhedra introduced by Martinetz (1993) for defining neighbourhood and topology preservation of feature maps