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	Biplot: Samtidig visning av rader och kolumner i multivariata data	Multidimensionell skalning (MDS)
Ämnesområde	Statistik	Statistik
Familj	Latent structure	Latent structure
Ursprungsår	1971	1952–1964
Upphovsperson	Ruben Gabriel	Warren S. Torgerson (metric MDS, 1952); Joseph B. Kruskal (non-metric MDS, 1964)
Typ	Multivariate graphical display	Dimensionality reduction / visualization
Ursprungskälla	Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58(3), 453–467.	Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1), 1–27.
Alias	Gabriel biplot, PCA biplot, JK biplot, Çift grafik	MDS, metric MDS, non-metric MDS, proximity scaling
Närliggande	2	5
Sammanfattning	A biplot is a low-dimensional graphical representation of a multivariate data matrix that simultaneously displays both the observations (rows) and the variables (columns) as points or vectors in the same plot. Introduced by Ruben Gabriel in 1971, the technique decomposes the data matrix into a rank-2 approximation using singular value decomposition, allowing the approximate value of any data entry to be read as the inner product of the corresponding row and column markers.	Multidimensional scaling maps objects described only by pairwise similarities or dissimilarities into a low-dimensional geometric space so that distances in that space reflect the original proximity structure as faithfully as possible. It is widely used to visualize the hidden structure of psychological, social, and behavioral data.