Multidimensional scaling
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a data set. MDS is used to translate distances between each pair of objects in a set into a configuration of points mapped into an abstract Cartesian space.[1]
More technically, MDS refers to a set of related ordination techniques used in information visualization, in particular to display the information contained in a distance matrix. It is a form of non-linear dimensionality reduction.
Given a distance matrix with the distances between each pair of objects in a set, and a chosen number of dimensions, N, an MDS algorithm places each object into N-dimensional space (a lower-dimensional representation) such that the between-object distances are preserved as well as possible. For N = 1, 2, and 3, the resulting points can be visualized on a scatter plot.[2]
Core theoretical contributions to MDS were made by James O. Ramsay of McGill University, who is also regarded as the founder of functional data analysis.[3]