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Multidimensional Scaling of Histogram Dissimilarities

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Data Science and Classification

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, 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 a histogram of dissimilarities by a histogram 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 Hist-Scal using iterative majorization, that is based on an algorithm, I-Scal developed for the case where the dissimilarities are given by a range of values ie an interval (see Groenen et al. (in press)). 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.

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© 2006 Springer-Verlag Berlin · Heidelberg

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Groenen, P.J.F., Winsberg, S. (2006). Multidimensional Scaling of Histogram Dissimilarities. In: Batagelj, V., Bock, HH., Ferligoj, A., Žiberna, A. (eds) Data Science and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34416-0_18

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