The geometry of biplot scaling

Gower, J. C. (2004). The geometry of biplot scaling. Biometrika, 91(3) pp. 705–714.



A simple geometry allows the main properties of matrix approximations used in biplot displays to be developed. It establishes orthogonal components of an analysis of variance, from which different contributions to approximations may be assessed. Particular attention is paid to approximations that share the same singular vectors, in which case the solution space is a convex cone. Two- and three-dimensional approximations are examined in detail and then the geometry is interpreted for different forms of the matrix being approximated.

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