Least Squares Multidimensional Scaling with Transformed Distances
We consider a general least squares loss function for multidimensional scaling. Special cases of this loss function are STRESS, S-STRESS, and MULTISCALE. Several analytic results are presented. In particular, we present the gradient and Hessian, and look at the differentiability at a local minimum. We also consider fulldimensional scaling and indicate when a global minimum can be obtained. Furthermore, we treat the problem of inverse multidimensional scaling, where the aim is to find those dissimilarity matrices for which a fixed configuration is a stationary point.
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