Multidimensional Scaling for Interval Data: INTERSCAL

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.

12 pages