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 σ_{n}^{[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 d_{ij}(Z).

4. Transform dissimilarities δ_{ij} into disparities d′_{ij}.

5. Standardize the disparities so that η_{d′}^{2} = n(n–1)/2.

6. Compute the Guttman transform X^{[k]} of Z.

7. Compute new distances d_{ij}(X^{[k]}).

8. Compute normalized stress σ_{n} (d′, X^{[k]})

9. If σ_{n}^{[k]} – σ_{n}^{[k–1]} / σ_{n}^{[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