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arXiv · 2401.05466

Multidimensional Scaling for Interval Data: INTERSCAL

Susanne Winsberg·Oldemar Rodriguez·Edwin Diday
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Abstract

Standard multidimensional scaling takes as input a dissimilarity matrix of general term $\delta _{ij}$ which is a numerical value. In this paper we input $\delta _{ij}=[\underline{\delta _{ij}},\overline{\delta _{ij}}]$ where $\underline{\delta _{ij}}$ and $\overline{\delta _{ij}}$ are the lower bound and the upper bound of the ``dissimilarity'' between the stimulus/object $S_i$ and the stimulus/object $S_j$ respectively. As output instead of representing each stimulus/object on a factorial plane by a point, as in other multidimensional scaling methods, in the proposed method each stimulus/object is visualized by a rectangle, in order to represent dissimilarity variation. We generalize the classical scaling method looking for a method that produces results similar to those obtained by Tops Principal Components Analysis. Two examples are presented to illustrate the effectiveness of the proposed method.

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Susanne Winsberg, Oldemar Rodriguez, Edwin Diday. 2024-01-10. Multidimensional Scaling for Interval Data: INTERSCAL. https://arxiv.org/abs/2401.05466

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