SymScal: symbolic multidimensional scaling of interval dissimilarities
AbstractMultidimensional scaling aims at reconstructing dissimilaritiesbetween pairs of objects by distances in a low dimensional space.However, in some cases the dissimilarity itself is unknown, but therange of the dissimilarity is given. Such fuzzy data fall in thewider class of symbolic data (Bock and Diday, 2000).Denoeux and Masson (2000) have proposed to model an intervaldissimilarity by a range of the distance defined as the minimum andmaximum distance between two rectangles representing the objects. Inthis paper, we provide a new algorithm called SymScal that is basedon iterative majorization. The advantage is that each iteration isguaranteed to improve the solution until no improvement is possible.In a simulation study, we investigate the quality of thisalgorithm. We discuss the use of SymScal on empirical dissimilarityintervals of sounds.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2005-15.
Date of creation: 30 Mar 2005
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iterative majorization; multidimensional scaling; symbolic data analysis; distance smoothing;
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- 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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