Penalized Full-dimensional Scaling

The theory of full-dimensional (metric, Euclidean, least squares) multidimensional scaling is combined with a penalty function approach with the purpose of finding global minima in low-dimensional multidimensional scaling. The paper also proves that stationary points of lower-dimensional MDS problems are saddle points of higher-dimensional MDS problems. This result is used to show that the SMACOF algorithm for full-dimensional MDS converges to the unique global minimum of the loss function.