This paper is about the ability of principal components analysis, the
Sammon algorithm, and an extension of the Kohonen self-organizing feat
ure map to preserve spatial order during feature extraction on unlabel
ed data. Transformations to q-space that preserve the order of all pai
rwise distances in any set of vectors in p-space are defined as metric
topology preserving (MTP) transformations. We give a necessary and su
fficient condition for this new property in terms of the Spearman rank
correlation coefficient. Unlike many other measures of extracted feat
ure quality, the MTP index is independent of the extraction method. A
modification of the Kohonen self-organizing feature map algorithm that
extracts vectors in q-space from data in p-space is developed. The ex
tent to which principal components, Sammon's algorithm and our extensi
on of the self-organizing feature map (SOFM) preserve the MTP property
is discussed. Our MTP index shows that the first two methods preserve
distance ranks on seven data sets much more effectively than extended
SOFM.