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 dij.
5. Standardize the disparities so that ηd2 = 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).


© djmw, January 19, 1998