Construction of SSA Representations

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.