With some network architectures it is possible to map high-dimensional input signals onto a lower-dimensional structure in such a way, that some similarity relations present in the original data are still present after the mapping. This has been denoted feature mapping and can be useful for data visualization. A prerequisite for this is that the network used has a fixed dimensionality. This is the case, e.g., for the self-organizing feature map and the other methods discussed in section 6 of this report.
A related question is, how topology-preserving is the mapping from the input data space onto the discrete network structure, i.e. how well are similarities preserved? Several quantitative measures have been proposed to evaluate this like the topographic product (Bauer and Pawelzik, 1992) or the topographic function (Villmann et al., 1994).