Chapter 3 Multidimensional Scaling (MDS)

The next two chapters continue the review of approaches to reduce the variable dimension of a problem, but now with a focus on so-called distance preserving methods. Such techniques aim to represent, or, more precisely, embed data points from a high-dimensional attribute space in a lower dimensional space (typically 2D or 3D) for easy visualization. The representation is such that the relative distances between the data points in attribute space are preserved as much as possible.

In the current chapter, the topic is
multidimensional scaling (MDS). Two major methods are considered, one based on an eigenvalue decomposition, the other on scaling by majorizing a complex function, or SMACOF. Each method is presented in some mathematical detail and its implementation is illustrated. A special emphasis continues to be on spatializing these methods, by focusing on the connection between attribute space and geographical space. A new measure of the match between spatial and attribute similarity is introduced as the common coverage percentage. In addition, the neighbor match test introduced in Volume 1 is extended to MDS solutions.

Some of the discussion is fairly technical and can be readily skipped if the main interest is in application and interpretation.

Again, the Italy Community Banks sample data set is used to illustrate these technique.