Abstract
The neighborhood preservation of self-organizing
feature maps like the Kohonen map is an important
property which is exploited in many applications.
However, if a dimensional conflict arises this property
is lost. Various qualitative and quantitative
approaches are known for measuring the degree of
topology preservation. They are based on using the
locations of the synaptic weight vectors. These
approaches, however, may fail in case of nonlinear data
manifolds. To overcome this problem, in this paper we
present an approach which uses what we call the induced
receptive fields for determining the degree of topology
preservation. We first introduce a precise definition
of topology preservation and then propose a tool for
measuring it, the topographic function. The topographic
function vanishes if and only if the map is topology
preserving. We demonstrate the power of this tool for
various examples of data manifolds
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