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An often encountered problem with multivariate data is that the data cannot be adequately displayed on 2-dimensional paper or computer screens. For more than two dimensions, we have to project the data onto a plane. This projection changes with its direction; or, in other words, the projected image changes if the data points are rotated in the n-dimensional space. One might now ask for a way how to find a particular rotation of the data which displays a maximum of information in the projected image.
The process to obtain a suitable projection for this purpose is called principal component analysis (PCA) and results in a rotation of the Cartesian coordinate system in such a way that the axes show a maximum of variation along their directions.