SymScal: symbolic multidimensional scaling of interval dissimilarities

Patrick Groenen (), S. Winsberg, O. Rodriguez and E. Diday

No EI 2005-15, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

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.

Keywords: distance smoothing; iterative majorization; multidimensional scaling; symbolic data analysis (search for similar items in EconPapers)
Date: 2005-03-30
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Citations: View citations in EconPapers (2)

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