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## Distance-Based Transformations of Biplots

- Author(s): de Leeuw, Jan
- et al.

## Abstract

In principal component analysis and related techniques, we approximate (in the least squares sense) as *n x m* matrix *F* by an *n x m* matrix *G* which satisfies rank(*G*) ≤ *p*, where *p* < min(*n,m*). Or equivalenty, we want to find an *n x p* matrix *X* and an *m x p* matrix *Y* such that *G* = *XY'* approximates *F* as closely as possible. The rows of *X* and *Y* are then often used in graphical displays. In particular, *biplots* represent *X* and *Y* jointly as *n + m* points in Euclidean *p* space.