Construct a principal surface that are two-dimensional surfaces that pass through the middle of a p-dimensional data set. They minimise the distance from the data points, and provide a nonlinear summary of data. The surfaces are nonparametric and their shape is suggested by the data. The formation of a surface is found using an iterative procedure which starts with a linear summary, typically with a principal component plane. Each successive iteration is a local average of the p-dimensional points, where an average is based on a projection of a point onto the nonlinear surface of the previous iteration. For more information on principal surfaces, see Ganey, R. (2019, "https://open.uct.ac.za/items/4e655d7d-d10c-481b-9ccc-801903aebfc8").