Multidimensional Scaling and Distance Geometry

Abstract

Imagine you have a map of a particular geographical region, which includes a number of cities and towns. Usually, such a map will be accompanied by a two-way table displaying how close a selected number of those towns and cities are to each other. Each cell of that table will show the degree of “closeness” (or proximity) of the row city to the column city that identifies that cell. The notion of proximity between two geographical locations is easy to understand, even though it could have different meanings: for example, proximity could be defined as straight-line distance or as shortest traveling distance.