Multidimensional Scaling Tool

Multidimensional Scaling (MDS) is a method of separating univariate data based upon variance. Conceptually, MDS takes the dissimilarities, or distances, between items described in the data and generates a map between the items. The number of dimensions in this map are often provided prior to generation by the analyst. Usually, the highest variance dimension corresponds to the largest distances being described in the data. The map solution relies on univariate data, so the rotation and orientation of the map dimensions are not significant. MDS uses dimensional analysis similar to Principle Components. For more information see https://en.wikipedia.org/wiki/Multidimensional_scaling.

Two types of MDS are implemented in this tool: Classical MDS, and Isometric MDS. Classical MDS is the simple and fast approach. Classical MDS works by generating a map by reducing the error between given distances between items and the cartesian distance between the items on the map. Isometric MDS is slightly more complex. If the resulting map of Classical MDS is taken and then adjusted so that the map distances between item pairs are in the same largest-to-smallest order as the original data, that is Isometric MDS. This Isometric MDS is then useful when the exact distance units are less important than the rank of which item pairs are farthest apart or closest together.

An example use of Classical MDS is the straight-line distance between cities across the USA to produce a map of the USA. An example use of Isometric MDS is producing a multidimensional food chart based on how similar or different the nutritional value is between food items, where a ranking of the distances is more important than a specific unit coordinate. These methods are often used in a marketing research context to obtain the number and nature of the perceptual dimensions used by customers to judge the similarity between different items.