S. Winsberg
http://repub.eur.nl/ppl/5116/
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RePub, Erasmus University Repository3WaySym-Scal: three-way symbolic multidimensional scaling
http://repub.eur.nl/pub/8172/
Tue, 05 Dec 2006 00:00:01 GMT<div>P.J.F. Groenen</div><div>S. Winsberg</div>
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 not known, but the range, or a histogram of the dissimilarities is given. This type of data fall in the wider class of symbolic data (see Bock and Diday (2000)). We model three-way two-mode data consisting of an interval of dissimilarities for each object pair from each of K sources by a set of intervals of the distances defined as the minimum and maximum distance between two sets of embedded rectangles representing the objects. In this paper, we provide a new algorithm called 3WaySym-Scal using iterative majorization, that is based on an algorithm, I-Scal developed for the two-way case where the dissimilarities are given by a range of values ie an interval (see Groenen et al. (2006)).
The advantage of iterative majorization is that each iteration is guaranteed to improve the solution until no improvement is possible. We present the results on an empirical data set on synthetic musical tones.I-Scal: Multidimensional scaling of interval dissimilarities
http://repub.eur.nl/pub/70520/
Wed, 01 Nov 2006 00:00:01 GMT<div>P.J.F. Groenen</div><div>S. Winsberg</div><div>P.M. RodrÃguez</div><div>E. Diday</div>
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 give rise to a data matrix in which each dissimilarity is an interval of values. These interval dissimilarities are modelled by the ranges of the distances defined as the minimum and maximum distance between two rectangles representing the objects. Previously, two approaches for such data have been proposed and one of them is investigated. A new algorithm called I-Scal is developed. Because I-Scal is based on iterative majorization it has the advantage that each iteration is guaranteed to improve the solution until no improvement is possible. In addition, a rational start configuration is proposed that is helpful in locating a good quality local minima. In a simulation study, the quality of this algorithm is investigated and I-Scal is compared with one previously proposed algorithm. Finally, I-Scal is applied on an empirical example of dissimilarity intervals of sounds.SymScal: symbolic multidimensional scaling of interval dissimilarities
http://repub.eur.nl/pub/1924/
Wed, 30 Mar 2005 00:00:01 GMT<div>P.J.F. Groenen</div><div>S. Winsberg</div><div>O. Rodriguez</div><div>E. Diday</div>
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.