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Multidimensional scaling
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<p>Multidimensional scaling (MDS) is a means of visualizing the level of <a href="/facts/Similarity_measure/FmmFco8c">similarity</a> of individual cases of a data set. MDS is used to translate distances between each pair of n {\textstyle n} objects in a set into a configuration of n {\textstyle n} points mapped into an abstract <a href="/facts/Cartesian_coordinate_system/lkTqvMmB">Cartesian space</a>. </p><p>More technically, MDS refers to a set of related <a href="/facts/Ordination_(statistics)/skxK9rUM">ordination</a> techniques used in <a href="/facts/Information_visualization/DSHteV85">information visualization</a>, in particular to display the information contained in a <a href="/facts/Distance_matrix/2ptk07Y7">distance matrix</a>. It is a form of <a href="/facts/Non-linear_dimensionality_reduction/1lL1Y0vN">non-linear dimensionality reduction</a>. </p><p>Given a distance matrix with the distances between each pair of objects in a set, and a chosen number of dimensions, <i>N</i>, an MDS <a href="/facts/Algorithm/fnl5NmRt">algorithm</a> places each object into <i>N</i>-<a href="/facts/Dimension/0ktmUyac">dimensional</a> space (a lower-dimensional representation) such that the between-object distances are preserved as well as possible. For <i>N</i> = 1, 2, and 3, the resulting points can be visualized on a <a href="/facts/Scatter_plots/n03xBtBL">scatter plot</a>. </p><p>Core theoretical contributions to MDS were made by <a href="/facts/James_O._Ramsay/twLYffe0">James O. Ramsay</a> of <a href="/facts/McGill_University/amouytVp">McGill University</a>, who is also regarded as the founder of <a href="/facts/Functional_data_analysis/dPLDWYHn">functional data analysis</a>. </p>