Summary
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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© 1996 Springer-Verlag Berlin · Heidelberg
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Groenen, P.J.F., de Leeuw, J., Mathar, R. (1996). Least Squares Multidimensional Scaling with Transformed Distances. In: Gaul, W., Pfeifer, D. (eds) From Data to Knowledge. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79999-0_17
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DOI: https://doi.org/10.1007/978-3-642-79999-0_17
Publisher Name: Springer, Berlin, Heidelberg
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