Fit a principal surface

Fits a two-dimensional principal surface to a numeric data matrix using the iterative expectation / projection algorithm of Hastie and Stuetzle (1989), with the coordinate functions estimated by local regression (loess).

Usage

prinsurf(X, max.iter = 10, span = 0.6, scale = FALSE, verbose = FALSE)

Arguments

X

A numeric matrix or data frame, \(n \times p\). Column names are used as variable names; if absent, V1, V2, ... are assigned.

max.iter

Maximum number of expectation/projection iterations.

span

The loess span (\(\alpha\)) used for the coordinate functions.

scale

Logical; if TRUE each variable is standardised to unit standard deviation before fitting (recommended when variables are on very different scales). Variables are always centred.

verbose

Logical; print the relative change and residual sum of squares at each iteration.

Value

An object of class "prinsurf": a list with elements lambda (the \(n \times 2\) surface coordinates of the samples), fj.mat (the fitted surface coordinates of the samples in the working units), models (the per-variable loess coordinate functions), varnames, center, scale, span and iterations.

References

Hastie, T. and Stuetzle, W. (1989) Principal curves. Journal of the American Statistical Association 84, 502–516.

Examples

set.seed(1)
s <- runif(120, -1, 1); t <- runif(120, -1, 1)
X <- cbind(x = s, y = t, z = 0.7 * s + 0.9 * t^2) +
     matrix(rnorm(360, 0, 0.03), 120, 3)
fit <- prinsurf(X, max.iter = 6)
fit
#> Principal surface fit: 120 samples, 3 variables
#>   loess span 0.60, converged in 4 iterations
#>   variables: x, y, z