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SymScal: symbolic multidimensional scaling of interval dissimilarities

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  • Groenen, P.J.F.
  • Winsberg, S.
  • Rodriguez, O.
  • Diday, E.

Abstract

Multidimensional scaling aims at reconstructing dissimilarities between pairs of objects by distances in a low dimensional space. However, in some cases the dissimilarity itself is unknown, but the range of the dissimilarity is given. Such fuzzy data fall in the wider class of symbolic data (Bock and Diday, 2000). Denoeux and Masson (2000) have proposed to model an interval dissimilarity by a range of the distance defined as the minimum and maximum distance between two rectangles representing the objects. In this paper, we provide a new algorithm called SymScal that is based on iterative majorization. The advantage is that each iteration is guaranteed to improve the solution until no improvement is possible. In a simulation study, we investigate the quality of this algorithm. We discuss the use of SymScal on empirical dissimilarity intervals of sounds.

Suggested Citation

  • Groenen, P.J.F. & Winsberg, S. & Rodriguez, O. & Diday, E., 2005. "SymScal: symbolic multidimensional scaling of interval dissimilarities," Econometric Institute Research Papers EI 2005-15, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1924
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    1. Suzanne Winsberg & J. Douglas Carroll, 1989. "A quasi-nonmetric method for multidimensional scaling VIA an extended euclidean model," Psychometrika, Springer;The Psychometric Society, vol. 54(2), pages 217-229, June.
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    4. Henk Kiers & Patrick Groenen, 1996. "A monotonically convergent algorithm for orthogonal congruence rotation," Psychometrika, Springer;The Psychometric Society, vol. 61(2), pages 375-389, June.
    5. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
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    Cited by:

    1. Pełka Marcin, 2019. "Assessment of the Development of the European Oecd Countries with the Application of Linear Ordering and Ensemble Clustering of Symbolic Data," Folia Oeconomica Stetinensia, Sciendo, vol. 19(2), pages 117-133, December.
    2. Hebert, Pierre-Alexandre & Masson, Marie-Helene & Denoeux, Thierry, 2006. "Fuzzy multidimensional scaling," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 335-359, November.

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