Abstract
By the use of simulated annealing it is defined the algorithm MDSI-SS for the optimization of Stress defined by Donoeux and Masson [6] for interval-type dissimilarities.On three data sets it is compared the value of stress obtained by MDSI-SS and INTERSCAL (the later is the algorithm proposed by Rodríguez et al. [12]).
References
Aarts, E.; Korst, J. (1989) Simulated Annealing and Boltzmann Machines. John Wiley & Sons, Chichester.
Bock, H-H.; Diday, E. (eds.) (2000) Analysis of Symbolic Data. Exploratory Methods for Extracting Statistical Information from Complex Data. Springer Verlag, Heidelberg.
Borg, I.; Groenen, P. (1997) Modern Multidimensional Scaling. Springer, New York.
Cazes, P.; Chouakria, A.; Diday, E.; Schektman, Y. (1997) “Extension de l’analyse en composantes principales à des données de type intervalle”, Rev. Statistique Appliquée 45(3): 5–24.
Cox, T.; Cox, M. (1994) Multidimensional Scaling. Chapman & Hall, London.
Denoeux, T.; Masson, M. (1999) “Multidinsional scaling of interval-valued dissimilarity data”. Université de Technologie de Compiègne, France.
Diday, E. (1998) “Symbolic data analysis: a mathematical framework and tool for data mining”, in: A. Rizzi, M. Vichi & H. Bock (Eds.): Advances in Data Science and Classification, Springer-Verlag, Heidelberg: 409–416.
Diday, E. (1999) An Introduction to Symbolic Data Analysis and its Application to the Sodas Project: Purpose, History and Perspective. Paris IX–Dauphine University, France.
Gower, J.C. (1966) “Some distances properties of laten root and vector methods using multivariate analysis”, Biometrika, 53: 325–338.
Trejos J. et al. (2000) “Application of simulated annealing in some multidimensional scaling problems”, in: Kiers et al. (Eds.): Data Analysis, Classification and Related Methods. Springer, Heidelberg: 297–302.
Raju, S.R.K. (1997) “Symbolic data analysis in cardiology”, in: E. Diday & K.C. Gowda (Eds.): Symbolic Data Analysis and its Applications, CEREMADE, Paris: 245–249.
Rodŕıguez, O.; Diday, E.; Winsberg, S. (2000) “Multidimensional scaling for interval data: INTERSCAL”, submitted paper.
Torgenson, W.S. (1958) Theory and Methods of Scaling. Wiley, New York.
Winsberg, S.; De Soete, G. (1997) “Multidimensional scaling with constrained dimensions: CONSCAL”, British Journal of Mathematical and Statistical Psychology, 50: 55–72.