Multidimensional scaling (MDS) is a set of related statistical techniques often used in information visualization

Information visualization

Information visualization is the interdisciplinary study of "the visual representation of large-scale collections of non-numerical information, such as files and lines of code in software systems, library and bibliographic databases, networks of relations on the internet, and so forth".- Overview...

 for exploring similarities or dissimilarities in data. MDS is a special case of ordination

Ordination (statistics)

In multivariate analysis, ordination is a method complementary to data clustering, and used mainly in exploratory data analysis . Ordination orders objects that are characterized by values on multiple variables so that similar objects are near each other and dissimilar objects are farther from...

. An MDS algorithm starts with a matrix

Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...

 of item–item similarities, then assigns a location to each item in N-dimensional space, where N is specified a priori

A priori

A priori is Latin for "from the former" or "from before", and may refer to:* A priori knowledge, justification or arguments. See a priori and a posteriori.* A priori , a type of constructed language...

. For sufficiently small N, the resulting locations may be displayed in a graph or 3D visualisation.
MDS algorithms fall into a taxonomy

Taxonomy

Taxonomy is the science of identifying and naming species, and arranging them into a classification. The field of taxonomy, sometimes referred to as "biological taxonomy", revolves around the description and use of taxonomic units, known as taxa...

, depending on the meaning of the input matrix:
Classical multidimensional scaling: Also known as Torgerson Scaling or Torgerson–Gower scaling, takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a loss function called strain.
Metric multidimensional scaling: A superset of classical MDS that generalizes the optimization procedure to a variety of loss functions and input matrices of known distances with weights and so on.