Linganisha mbinu

	Ramani ya Utambuzi na Upendeleo	Biplot: Onyo la Wakati Huu wa Safu na nguzo katika Data za Multivariate
Nyanja	Takwimu	Takwimu
Familia	Latent structure	Latent structure
Mwaka wa asili	1979	1971
Mwanzilishi	John Hauser & Frank Koppelman	Ruben Gabriel
Aina	Multivariate spatial representation	Multivariate graphical display
Chanzo asilia	Hauser, J. R., & Koppelman, F. S. (1979). Alternative perceptual mapping techniques: Relative accuracy and usefulness. Journal of Marketing Research, 16(4), 495–506.	Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58(3), 453–467.
Majina mbadala	Perceptual Mapping, Preference Mapping, Attribute-Based Mapping, Algısal Haritalama	Gabriel biplot, PCA biplot, JK biplot, Çift grafik
Zinazohusiana	3	2
Muhtasari	Perceptual and preference mapping is a family of multivariate techniques that simultaneously positions competing objects—brands, products, or stimuli—and respondent preferences within a common low-dimensional space. Introduced systematically by Hauser and Koppelman (1979), the approach lets researchers visualize how consumers perceive attribute-level similarities among objects and which attributes drive individual or segment-level choice. It is widely used in market research, sensory science, and strategic positioning analysis.	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.