Procrustes

Description

The Procrustes function computes an orthogonal transformation matrix that aligns two matrices (X1 and X2) by minimizing the Frobenius norm of their difference. This transformation ensures that X2 is rotated to best match X1.

Procrustes <- function(X1,X2){
  #Return Omega = arg min||X1 - X2 Omgea||_F
  H = t(X2)%*%X1
  mod = svd(H)
  return(mod$u%*%t(mod$v))
}

Arguments

• X1: A matrix to be used as the reference for alignment.
• X2: A matrix to be transformed and aligned with X1.

Output

• Returns an orthogonal transformation matrix Ω such that \(\left \| X1-X2 \Omega \right\| _F\) is minimized.

See also

See BONMI_package for code example.