475
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Multidimensional scaling with city‐block distances based on combinatorial optimization and systems of linear equations

Pages 259-270 | Received 30 Sep 2008, Published online: 14 Oct 2010

References

  • Arabie , P. 1991 . Was Euclid an unnecessarily sophisticated psychologist? . Psychometrika, , 56 (4) : 567 – 587 . (doi:10.1007/BF02294491)
  • Baravykaite , M. and Čiegis , R. 2007 . An implementation of a parallel generalized branch and bound template . Math. Model. Anal., , 12 (3) : 277 – 289 . (doi:10.3846/1392–6292.2007.12.277–289)
  • Baravykaite , M. , Čiegis , R. and ÂŽilinskas , J. 2005 . Template realization of generalized branch and bound algorithm . Math. Model. Anal., , 10 (3) : 217 – 236 .
  • Borg , I. and Groenen , P.J.F. 2005 . Modern Multidimensional Scaling: Theory and Applications. , 2nd edition , New York : Springer .
  • Brusco , M.J. 2001 . A simulated annealing heuristic for unidimensional and multidimensional (city‐block) scaling of symmetric proximity matrices . Journal of Classification, , 18 (1) : 3 – 33 . (doi:10.1007/s00357–001–0003–4)
  • Cox , T.F. and Cox , M.A.A. 2001 . Multidimensional Scaling, , 2nd edition , Boca Raton : Chapman & Hall/CRC .
  • de Leeuw , J. 1984 . Differentiability of Kruskal's stress at a local minimum . Psychometrika, , 49 (1) : 111 – 113 . (doi:10.1007/BF02294209)
  • Green , P. , Carmone , F. and Smith , S. 1989 . Multidimensional Scaling: Concepts and Applications. , Boston : Allyn and Bacon .
  • Groenen , P.J.F. , Mathar , R. and Heiser , W.J. 1995 . The majorization approach to multidimensional scaling for Minkowski distances . Journal of Classification, , 12 (1) : 3 – 19 . (doi:10.1007/BF01202265)
  • Hwa , J. , Graham , R.M. and Perez , D.M. 1995 . Identification of critical determinants of α1‐adrenergic receptor subtype selective agonist binding . Journal of Biological Chemistry, , 270 (39) : 23189 – 23195 .
  • Leung , P.L. and Lau , K. 2004 . Estimating the city‐block two‐dimensional scaling model with simulated annealing . European Journal of Operational Research, , 158 (2) : 518 – 524 . (doi:10.1016/S0377–2217(03)00357–6)
  • Ruuskanen , J.O. , Laurila , J. , Xhaard , H. , Rantanen , V.‐V. , Vuoriluoto , K. , Wurster , S. , Marjamäki , A. , Vainio , M. , Johnson , M. S. and Scheinin , M. 2005 . Conserved structural, pharmacological and functional properties among the three human and five zebrafish α2‐adrenoceptors . British Journal of Pharmacology, , 144 (2) : 165 – 177 . (doi:10.1038/sj.bjp.0706057)
  • Varoneckas , A. , ÂŽilinskas , A. and ÂŽilinskas , J. 2008 . Parallel multidimensional scaling using grid computing: assessment of performance . Information Technology and Control, , 37 (1) : 52 – 56 .
  • Vera , J.F. , Heiser , W.J and Murillo , A. 2007 . Global optimization in any Minkowski metric: a permutation‐translation simulated annealing algorithm for multidimensional scaling . Journal of Classification, , 24 (2) : 277 – 301 . (doi:10.1007/s00357–007–0020–1)
  • ÂŽilinskas , A. and ÂŽilinskas , J. 2006 . On visualization of multidimensional data using three‐dimensional embedding space . Technological and Economic Development of Economy, , 12 (4) : 353 – 359 .
  • ÂŽilinskas , A. and ÂŽilinskas , J. 2006 . Parallel hybrid algorithm for global optimization of problems occurring in MDS based visualization . Computers & Mathematics with Applications, , 52 (1–2) : 211 – 224 . (doi:10.1016/j.camwa.2006.08.016)
  • 2009 . Math. Model. Anal. , 14 (2) : 259 – 270 .
  • ÂŽilinskas , A. and ÂŽilinskas , J. 2007 . Parallel genetic algorithm: assessment of performance in multidimensional scaling . GECCO ‘07: Proceedings of the 9th annual conference on Genetic and evolutionary computation . 2007 . pp. 1492 – 1501 . ACM . (doi:10.1145/1276958.1277229)
  • ÂŽilinskas , A. and ÂŽilinskas , J. 2007 . Two level minimization in multidimensional scaling . Journal of Global Optimization, , 38 (4) : 581 – 596 . (doi:10.1007/s10898–006–9097‐x)
  • ÂŽilinskas , A. and ÂŽilinskas , J. 2008 . A hybrid method for multidimensional scaling using city‐block distances . Mathematical Methods of Operations Research, , 68 (3) : 429 – 443 . (doi:10.1007/s00186–008–0238–5)
  • ÂŽilinskas , A. and ÂŽilinskas , J. Three‐dimensional visualization by means of multidimensional scaling . The 20th International Conference EURO Mini Conference Continuous Optimization and Knowledge‐Based Technologies (EurOPT‐2008 . May 20–23 2008 , Neringa, Lithuania. Edited by: Sakalauskas , L. , Weber , G. W. and Zavadskas , E.K. pp. 71 – 76 .
  • ÂŽilinskas , A. and ÂŽilinskas , J. 2009 . Branch and bound algorithm for multidimensional scaling with city‐block metric . Journal of Global Optimization, , 43 (2–3) : 357 – 372 . (doi:10.1007/s10898–008–9306‐x)
  • ÂŽilinskas , A. , ÂŽilinska , J. and Optimization‐based , S. 2009 . “ visualization ” . In Encyclopedia of Optimization , 2nd edition , Edited by: Floudas , C. A. and Pardalos) , P.M. 2785 – 2791 . Springer . (doi:10.1007/978–0–387–74759–0_478)
  • ÂŽilinskas , J. 2006 . “ Multidimensional scaling in protein and pharmacological sciences ” . In Computer Aided Methods in Optimal Design and Operations , Edited by: Bogle , I. D. L. and ÂŽilinskas , J. 139 – 148 . World Scientific .
  • ÂŽilinskas , J. 2007 . Reducing of search space of multidimensional scaling problems with data exposing symmetries . Information Technology and Control, , 36 (4) : 377 – 382 .
  • ÂŽilinskas , J. 2008 . Branch and bound with simplicial partitions for global optimization . Math. Model. Anal., , 13 (1) : 145 – 159 . (doi:10.3846/1392–6292.2008.13.145–159)
  • ÂŽilinskas , J. 2008 . On dimensionality of embedding space in multidimensional scaling . Informatica, , 19 (3) : 447 – 460 .
  • ÂŽilinskas , J. 2009 . “ Parallel global optimization in multidimensional scaling. ” . In Parallel Scientific Computing and Optimization , Edited by: Čiegis , R. , Henty , D. , Kågström , B. and ÂŽilinskas , J. volume 27 , 69 – 82 . Springer Optimization and Its Applications . Springer (doi:10.1007/978–0–387–09707–7_6)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.