方法对比

	双标图：多元数据中行和列的同时显示	对应分析	多维尺度分析 (MDS)
领域	统计学	统计学	统计学
方法族	Latent structure	Latent structure	Latent structure
起源年份	1971	1984	1952–1964
提出者	Ruben Gabriel	Jean-Paul Benzécri; Michael Greenacre	Warren S. Torgerson (metric MDS, 1952); Joseph B. Kruskal (non-metric MDS, 1964)
类型	Multivariate graphical display	Exploratory multivariate technique for categorical data	Dimensionality reduction / visualization
开创性文献	Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58(3), 453–467.	Greenacre, M. J. (1984). Theory and Applications of Correspondence Analysis. Academic Press. ISBN: 978-0-12-299050-2	Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1), 1–27.
别名	Gabriel biplot, PCA biplot, JK biplot, Çift grafik	CA, Simple Correspondence Analysis, Reciprocal Averaging, Karşılıklı Uyum Analizi	MDS, metric MDS, non-metric MDS, proximity scaling
相关	2	2	5
摘要	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.	Correspondence Analysis (CA) is an exploratory multivariate technique for visualizing the association structure of a two-way contingency table. Developed systematically by Jean-Paul Benzécri in France during the 1960s–1970s and brought to an English-language audience by Michael Greenacre in 1984, CA decomposes the chi-square statistic of a cross-tabulation to produce a low-dimensional joint display — called a biplot — in which rows and columns are represented as points whose proximities reflect their associations.	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.