Multidimensional Scaling

Multidimensional scaling (MDS) is a tool through which the level of relationship of individual cases of a dataset can be visualized. It denotes to a set of associated ordination methods employed in data visualization, specifically to show the information confined in a distance matrix. Main objective of an MDS algorithm is to place each object in N-dimensional space such that the between-object distances are conserved as much as possible. Each object is then allocated coordinates in each of the N dimensions. In general, the more dimensions we use to reproduce the distance matrix, the better is the fit of the reproduced matrix to the observed matrix. If we use as many dimensions as there are variables, then the observed distance matrix can be reproduced perfectly. Of course, our objective is to minimize the observed complexity of nature, that is, to explain the distance matrix in terms of fewer underlying dimensions.

The final step of the analysis is the interpretation of dimensions. The actual alignments of the axes from the MDS analysis are random, and can be revolved in any direction. A first step is to generate scatterplots of the objects in the different two-dimensional planes. Three-dimensional solutions can also be demonstrated graphically; but, their analysis is a bit complex. In addition to "meaningful dimensions," one can also look for clusters of points or particular arrays and configurations.