方法对比

	双标图：多元数据中行和列的同时显示	对应分析	多重对应分析 (MCA)
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	2006
提出者	Ruben Gabriel	Jean-Paul Benzécri; Michael Greenacre	Greenacre & Blasius
类型	Multivariate graphical display	Exploratory multivariate technique for categorical data	Multivariate exploratory ordination
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	Greenacre, M., & Blasius, J. (Eds.). (2006). Multiple Correspondence Analysis and Related Methods. Chapman & Hall/CRC. ISBN: 978-1-58488-628-0
别名	Gabriel biplot, PCA biplot, JK biplot, Çift grafik	CA, Simple Correspondence Analysis, Reciprocal Averaging, Karşılıklı Uyum Analizi	MCA, Homogeneity Analysis, Multiple Nominal Component Analysis, Çoklu Uyum Analizi
相关	2	2	2
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.	Multiple Correspondence Analysis (MCA) is a multivariate ordination technique designed to explore and visualize associations among three or more categorical variables simultaneously. By mapping both observations and variable categories onto a shared low-dimensional space, MCA reveals hidden structure in nominal or ordinal survey data. The method was comprehensively systematized and extended by Michael Greenacre and Jorg Blasius in their 2006 edited volume, building on earlier geometric data analysis traditions developed in France by Jean-Paul Benzecri during the 1960s and 1970s.