Multidimensional Scaling of Distributional Data
Yoshikazu Terada, Patrick J. F. Groenen · 2022
Multidimensional scaling (MDS) is a technique that visualizes dissimilarities between pairs of objects as distances between points in a low dimensional space. Standard MDS assumes that a single value of the dissimilarity is given for each pair of objects. To handle distributions of dissimilarities, histogram MDS has been proposed in Groenen and Winsberg (2007). They build on histograms of the empirical distributions of the dissimilarity of each of the pairs of objects. They also make use of so-called symbolic MDS for interval dissimilarities. The third ingredient of histogram MDS is the use of three-way MDS for several nested intervals that together describe the histograms. This chapter provides an overview of models for distributional dissimilarities by histogram MDS. Instead of representing an object by a single point in a low dimensional space, histogram MDS depicts objects as (concentric) circles or rectangles. The various models and their ingredients are illustrated by empirical examples.