Multidimensional Scaling (MDS)

Multidimensional scaling (MDS) is a technique for generating coordinate spaces from distance or (dis)similarity data. Consider, for instance, a distance chart such as one often found on a road map, containing the travel distances between towns and cities. If we had such a distance chart but not the associated map, MDS could be used to “re-create” the map of towns and cities. In an MDS, however, the distances in the chart do not have to be travel distances. They can be any sort of “distance,” such as the perceived differences between political candidates, differences between neighborhoods, art styles, technology companies, stocks, political parties, and so on. MDS uses these distances as input and attempts to construct the corresponding map. With MDS, one can create spatial representations of complex, multidimensional concepts and phenomena.

MDS is a member of a family of techniques known as ordination techniques. Ordination refers to the grouping of the variables or attributes describing a set of objects into a smaller, more essential set of so-called factors or dimensions. Other ordination techniques are factor analysis, principal components analysis, correspondence analysis, discriminant analysis, and conjoint analysis. Which technique to use depends on the nature of the available data and the specific ordination task at hand.

Although MDS is rarely used to make real geographical maps (an interesting example is discussed later), the fact that MDS can make a map from a set of distances or (dis)similarities has been used on many occasions where the distances are not geographical distances, but rather differences or dissimilarities between things. For instance, in a famous experiment by Rothkopf, subjects listened to two randomly selected Morse signals played in quick succession and were then asked to rate the similarity between those two signals. By applying MDS to the similarity data, first Sheppard and later Kruskal and Wish were able to make a “map” of the signals, and by studying how the various signals were laid out on the map, they were able to conclude that people's perceptions of Morse signals are determined by only two factors or dimensions: the length of the signal, measured as the number of dots and dashes it contains, and the relative number of dots versus dashes in the signal (see Figure 1). Similarly, researchers have used MDS to uncover the basic dimensions of a great variety of other phenomena, such as residential neighborhood characterization, sexual harassment, science citations, and information system usage.