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	Multiple Correspondence Analysis (MCA)（多重対応分析）
分野	統計学	統計学
系統	Latent structure	Latent structure
提唱年	1971	2006
提唱者	Ruben Gabriel	Greenacre & Blasius
種類	Multivariate graphical display	Multivariate exploratory ordination
原典	Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58(3), 453–467.	Greenacre, M., & Blasius, J. (Eds.). (2006). Multiple Correspondence Analysis and Related Methods. Chapman & Hall/CRC. ISBN: 978-1-58488-628-0
別名	Gabriel biplot, PCA biplot, JK biplot, Çift grafik	MCA, Homogeneity Analysis, Multiple Nominal Component Analysis, Çoklu Uyum Analizi
関連	2	2
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.	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.