Multidimensional Definition and 47 Threads

Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of



n


{\textstyle n}
objects or individuals" into a configuration of



n


{\textstyle n}
points mapped into an abstract Cartesian space.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.Core theoretical contributions to MDS were made by James O. Ramsay of McGill University, who is also regarded as the father of functional data analysis.

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