Ordinal SSA by Iterative Optimization

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 2 in Multidimensional Similarity Structure Analysis, 1987, pp 12-27 from Springer

Abstract: Abstract We consider how to solve an ordinal SSA problem by computation. First, an arbitrary configuration is chosen and each of its points is defined to represent a particular object of observation. Then, the distances are measured, and their order is compared with the order of the data. By permuting the distances into the order of the data, we obtain the rank images. They are used to determine the necessary point movements. The movements can be expressed in terms of analytical geometry, where distances are computed from the point coordinates rather than measured from the configuration. This allows formulation of an optimization procedure that can be programmed for a computer.

Keywords: geometric representation; representation space; m-dimensional space; force vector; resultant force; target distance; permutation; rank image; motion vector; correction matrix; cycle; iterative approximation procedure; conjoint and disjoint distances; conditional and unconditional data; row- and column-conditional approach; rectangular coordinate system; constructive and analytical geometry; n-tuple; projection; coordinate axis; dimension; correction factor; position vector; free vector; image diagram. (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4612-4768-5_2

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