**Multidimensional Scaling:**

Multidimensional scaling (MDS) is an approach to multivariate analysis aimed at producing a spatial or geometrical representation of complex data.

MDS helps to explain the observed distance matrix or dissimilarity matrix for a set of N objects in terms of a much smaller number (m<<N) of underlying dimensions. It represents N objects in a Euclidean space with a small number of dimensions, e.g on a plane (m=2). The major criteria for such allocation is that pairwise distances of objects in this space are close to the corresponding elements of the initial distance matrix.

MDS is very popular in psychological and marketing research, where human perception is of interest. Suppose, for example, the elements of the distance matrix are subjective scores for distinction between taste of pairs of N=10 brands of coffee, averaged over several "tasters". Then, MDS can help to represent the 10 brands of coffee as points on a plane in such a way that brands that are perceived as being similar are plotted close together, and brands that are perceived as being different are plotted farther apart.