手法を比較

	多変量データにおける行と列の同時表示：バイプロット	多次元尺度構成法 (MDS)
分野	統計学	統計学
系統	Latent structure	Latent structure
提唱年	1971	1952–1964
提唱者	Ruben Gabriel	Warren S. Torgerson (metric MDS, 1952); Joseph B. Kruskal (non-metric MDS, 1964)
種類	Multivariate graphical display	Dimensionality reduction / visualization
原典	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.
別名	Gabriel biplot, PCA biplot, JK biplot, Çift grafik	MDS, metric MDS, non-metric MDS, proximity scaling
関連	2	5
概要	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.