Procrustes transform

Source: R/procrustes.R

Procrustes transform Y = pXR (after centering), where p is a scaling coefficient and R is a rotation matrix that minimize ||Y - pXR||_F.

procrustes(Y, X, n_iter_max = 1000, epsilon_min = 1e-07)

Arguments

Y

Reference matrix.

X

Matrix to transform (ncol(X) >= ncol(Y)).

n_iter_max

Maximum number of iterations. Default is 1000.

epsilon_min

Convergence criterion. Default is 1e-7.

Value

Object of class "procrustes", a list with the following elements:

  • $R: the rotation matrix to apply to X,

  • $rho: the scaling coefficient to apply to X,

  • $c: the column centering to apply to the resulting matrix,

  • $diff: the average difference between Y and X transformed.

You can use method predict() to apply this transformation to other data.

Examples

A <- matrix(rnorm(200), ncol = 20)
B <- matrix(rnorm(length(A)), nrow = nrow(A))

proc <- procrustes(B, A)
str(proc)
#> List of 4
#>  $ R   : num [1:20, 1:20] 0.3607 -0.3925 0.2973 -0.0806 0.0411 ...
#>  $ rho : num 0.942
#>  $ c   : num [1, 1:20] 0.184 0.422 0.555 0.352 -0.107 ...
#>  $ diff: num 0.177
#>  - attr(*, "class")= chr "Procrustes"
plot(B, predict(proc, A)); abline(0, 1, col = "red")