Journal of Classification

, Volume 22, Issue 1, pp 119–138

A Permutation-Translation Simulated Annealing Algorithm for L1 and L2 Unidimensional Scaling

  • Alex Murillo
  • J. Fernando Vera
  • Willem J. Heiser
Article

DOI: 10.1007/s00357-005-0008-5

Cite this article as:
Murillo, A., Vera, J. & Heiser, W. Journal of Classification (2005) 22: 119. doi:10.1007/s00357-005-0008-5

Abstract

Given a set of objects and a symmetric matrix of dissimilarities between them, Unidimensional Scaling is the problem of finding a representation by locating points on a continuum. Approximating dissimilarities by the absolute value of the difference between coordinates on a line constitutes a serious computational problem. This paper presents an algorithm that implements Simulated Annealing in a new way, via a strategy based on a weighted alternating process that uses permutations and point-wise translations to locate the optimal configuration. Explicit implementation details are given for least squares loss functions and for least absolute deviations. The weighted, alternating process is shown to outperform earlier implementations of Simulated Annealing and other optimization strategies for Unidimensional Scaling in run time efficiency, in solution quality, or in both.

Copyright information

© Springer Science+Business Media Inc. 2005

Authors and Affiliations

  • Alex Murillo
    • 1
  • J. Fernando Vera
    • 2
  • Willem J. Heiser
    • 3
  1. 1.Costa-Rica UniversityCosta Rica
  2. 2.Granada UniversitySpain
  3. 3.Leiden UniversityThe Netherlands