3WaySym-Scal: three-way symbolic multidimensional scalingPatrick Groenen () and
S. Winsberg
No EI 2006-49 Revision_Date: 2009-07-29, Econometric Institute Report from Erasmus University Rotterdam, 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 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. Keywords: multidimensional scaling; three-way data; interval data; symbolic data analysis; 2WaySym-Scal (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: http://EconPapers.repec.org/RePEc:dgr:eureir:1765008172 Access Statistics for this paper More papers in Econometric Institute Report from Erasmus University Rotterdam, Econometric Institute |
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