Applications of combinatorial programming to data analysis: Seriation using asymmetric proximity measures

Authors:
  • FBFrank B. Baker
    Frank B. Baker
  • LHLawrence J. Hubert
    Lawrence J. Hubert
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Abstract
Based on a given asymmetric proximity function, a two‐stage computational heuristic for sequencing a set of objects along a continuum is presented and illustrated with the type of example common in the paired‐comparison literature. The first stage, defined by the pairwise interchange of objects, is intended to generate reasonably good orderings from randomly chosen initial starts; the second stage can be considered to be a refinement phase and depends on a general condition for an optimal solution suggested by Younger involving the interchange of consecutively placed groups of objects. An extension of the heuristic is also described that allows the selection and sequencing of a subset of all the possible objects.