So sánh phương pháp

	Biplot: Biểu diễn đồng thời hàng và cột trong dữ liệu đa biến	Mở rộng quy mô đa chiều (MDS)
Lĩnh vực	Thống kê	Thống kê
Họ	Latent structure	Latent structure
Năm ra đời	1971	1952–1964
Người khởi xướng	Ruben Gabriel	Warren S. Torgerson (metric MDS, 1952); Joseph B. Kruskal (non-metric MDS, 1964)
Loại	Multivariate graphical display	Dimensionality reduction / visualization
Công trình gốc	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.
Tên gọi khác	Gabriel biplot, PCA biplot, JK biplot, Çift grafik	MDS, metric MDS, non-metric MDS, proximity scaling
Liên quan	2	5
Tóm tắt	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.