Multidimensional Scaling Technique
What is Multidimensional Scaling?
- Multidimensional scaling is a visual representation of distances or dissimilarities between sets of objects. “Objects” can be colors, faces, map coordinates, political persuasion, or any kind of real or conceptual stimuli (Kruskal and Wish, 1978).
- Objects that are more similar (or have shorter distances) are closer together on the graph than objects that are less similar (or have longer distances). As well as interpreting dissimilarities as distances on a graph, MDS can also serve as a dimension reduction technique for high-dimensional data (Buja et. al, 2007).
A Simple Example
Multidimensional scaling uses a square, symmetric matrix for input. The matrix shows relationships between items. For a simple example, let’s say you had a set of cities in Florida and their distances:
The scaling produces a graph like the one below.
The very simple example above shows cities and distances, which are easy to visualize as a map. However, multidimensional scaling can work on “theoretically” mapped data as well. For example, Kruskal and Wish (1978) outlined how the method could be used to uncover the answers to a variety of questions about people’s viewpoints on political candidates. This could be achieved by reducing the data and issues (say, partisanship and ideology) to a two-dimensional map.
