Construction of SSA Representations

I. Borg and J. Lingoes
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I. Borg: Justus-Liebig-Universität, Department of Psychology
J. Lingoes: University of Michigan, Computing Center

Chapter 1 in Multidimensional Similarity Structure Analysis, 1987, pp 1-11 from Springer

Abstract: Abstract On a geographical map, the distances between ten cities are measured. We then attempt to reconstruct the original configuration of the cities from these distances. The reconstruction involves some ad hoc specifications because the resulting configuration can be be arbitrarily rotated, reflected, shifted, and dilated (similarity transformations). If the conditions for the reconstruction task axe weakened so that only the rank order, not the ratios, of the data values matter, almost the same solution is found. Transformations which preserve the order of the distances are now admissible, but in practice permit few additional point movements relative to the similarity transformations.

Keywords: configuration; mapping; distance; construction; ratio of distances; scale factor; solution; point set; reconstruction; rotation; reflection; transformation; rigid motion; translation; admissible/non-admissible transformation; dilation; similarity transformation; invariance; isometric transformation; proximities; ratio scaling; ranking number; solution set; solution space; indeterminate; representation; empty solution set; ratio SSA; ordinal SSA; nonmetric SSA; ordinal data; metric information; pairs of points; pairs of pairs of points; isotonic transformation; isotonic region (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4612-4768-5_1

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