smacof

Scaling by Majorizing a Complicated Function, the iterative algorithm to find an optimal Configuration.

  1. Initialize
  1.a. Get initial Configuration Z
  1.b. Set stress σn[0] to a very large value.
  1.c. Set iteration counter k = 0
  2. Increase iteration counter by one: k = k + 1
  3. Calculate distances dij(Z).
  4. Transform dissimilarities δij into disparities d′ij.
  5. Standardize the disparities so that ηd′2 = n(n–1)/2.
  6. Compute the Guttman transform X[k] of Z.
  7. Compute new distances dij(X[k]).
  8. Compute normalized stress σn (d′, X[k])
  9. If |σn[k] – σn[k–1]| / σn[k–1] < ε or k > maximumNumberOfIterations, then stop
  10. Set Z = X[k], and go to 2.

This algorithm goes back to De Leeuw (1977).