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.
Categories: stat.ME