Multidimensional Scaling for Interval Data: INTERSCAL

TL;DR

This paper introduces INTERSCAL, a multidimensional scaling method for interval dissimilarities that visualizes objects as rectangles to represent uncertainty, generalizing classical scaling and aligning with PCA results.

Contribution

The paper proposes a novel multidimensional scaling approach for interval data, visualizing objects as rectangles to capture dissimilarity uncertainty, extending classical methods.

Findings

Effectively visualizes interval dissimilarities as rectangles.

Produces results similar to PCA for data with uncertainty.

Demonstrated with two illustrative examples.

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.