A permutation-translation simulated annealing algorithm for L1 and L2 unidimensional scaling

Journal of Classification

Volumn 22, Issue 1, 2005, Pages 119-138

  Murillo, Alex ^a   Vera, J Fernando ^b,d   Heiser, Willem J ^c  

^a UNIVERSIDAD DE COSTA RICA   (Costa Rica)

^b UNIVERSITY OF GRANADA   (Spain)

^c LEIDEN UNIVERSITY   (Netherlands)

^d UNIVERSITY OF GRANADA   (Spain)

Author keywords

Permutation; Quadratic assignment; Simulated annealing; Translation; Unidimensional scaling

Indexed keywords

EID: 23044452763     PISSN: 01764268     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00357-005-0008-5     Document Type: Review

References (23)

1. AARTS, E. and KORST, J. (1989), Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing, Chichester [UK]; New York: Wiley
2. ANDRIEU, C. and DOUCET, A. (1998), Simulated Annealing for Bayesian Estimation of Hidden Markov Models, Tr 317, Department of Engineering, University of Cambridge.
3. BEARDEN, J.N. (2001), SASCAL: A Simulated Annealing Algorithm for Multidimensional Scaling, Technical report, Department of Psychology. The University of Maryland at College Park., College Park, MD 20742, USA.
4. BRUSCO, M.J. (2001), "A Simulated Annealing Heuristic for Unidimensional and Multidimensional (City-Block) Scaling of Symmetric Proximity Matrices," Journal of Classification, 18, 3-33.
5. BRUSCO, M.J. (2002), "Integer Programming Methods for Seriation and Unidimensional Scaling of Proximity Matrices. A Review and Some Extensions," Journal of Classification, 19, 45-67.
6. BRUSCO, M.J. and STAHL, S. (2000), "Using Quadratic Assignment Methods to Generate Initial Permutations for Least-Squares Unidimensional Scaling of Symmetric Proximity Matrices," Journal of Classification, 17, 197-223.
7. ČERNY, V. (1985), "Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulation Algorithm," Journal of Optimization Theory and Applications, 45, 41-51.
8. DE SOETE, G., HUBERT, L.J., and ARABIE, P. (1988), "The Comparative Performance of Simulated Annealing on Two Problems of Combinatorial Data Analysis," in Data Analysis and Informatics (Vol. 5), Ed., E. Diday, Amsterdam: North Holland, 489-496.
9. DEFAYS, D. (1978), "A Short Note on a Method of Seriation," British Journal of Mathematical and Statistical Psychology, 31, 49-53.
10. DUFLO, M. (1996), Random Iterative Models. Applications of Mathematics. 1., Volume 34, Berlin; New York: Springer-Verlag.
11. GEMAN, S. and GEMAN, D. (1984), "Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
12. HÀJEK, B. (1988), "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, 13, 311-329.
13. HUBERT, L.J., ARABIE, P., and MEULMAN, J. (2002), "Linear Unidimensional Scaling in the L2-norm: Basic Optimization Methods Using MATLAB," Journal of Classification, 19, 303-328.
14. KIRKPATRICK, S., GELATT, D., and VECCHI, M.P. (1983), "Optimization by Simulated Annealing," Science, 220, 671-680.
15. METROPOLIS, N.A., ROSENBLUTH, M., ROSENBLUTH, A., TELLER, A., and TELLER, E. (1953), "Equation of State Calculations by Fast Computing Machines," Journal of Chemical Physics, 21, 1087-1092.
16. MITRA, D., ROMEO, F., and SANGIOVANNI-VINCENTELLI, A. (1986), "Convergence and Finite-Time Behaviour of Simulated Annealing," Advances in Applied Probability, 18, 747-771.
17. PIZA, E., TREJOS, J., and MURILLO, A. (2002), "Combinatorial Optimization Heuristics in Partitioning with Non Euclidean Distances," Investigación Operacional, 23 (1), 3-14.
18. PLINER, V. (1996), "Metric Unidimensional Scaling and Global Optimization," Journal of Classification, 13, 3-18.
19. ROTHKOPF, E.A. (1957), "A Measure of Stimulus Similarity and Errors in Some Paired Associate Learning," Journal of Experimental Psychology, 53, 94-101.
20. SHEPARD, R.N., KILPATRIC, D.W., and CUNNINGHAM, J.P. (1975), "The Internal Representation of Numbers," Cognitive Psychology, 7, 82-138.
21. TREJOS, J., MURILLO, A., and PIZA, E. (1998), "Global Stochastic Optimization for Partitioning," in Advances in Data Science and Classification, Eds., A. Rizzi, M. Vichi, and H.-H. Bock, Heidelberg: Springer, 185-190.
22. VAN LAARHOVEN, P.J. and AARTS, E.H.L. (1987), Simulated Annealing: Theory and Applications, Dordrecth, The Netherlands: D. Reidel Publishing Company.
23. WINKLER, G. (1995), Image Analysis, Random Fields and Dynamic Monte Carlo Methods, New York: Springer-Verlag.