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Fig. 3.9. Approximating nonlinear distributions with principal curves and folding. (a) The principal curve passes through the middle of the data distribution, providing a more detailed representation of nonlinear distributions than principal components. Each point on the curve is positioned at the center of gravity of the part of the distribution enclosed within two infinitesimally close normals (Ritter et al. 1992). (b) If a more detailed representation of the thickness of the distribution is desired, the curve can be folded in the higher dimension.