Least squares multidimensional scaling with transformed distances
Authors
Abstract
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.
BibTEX Reference Entry
@inbook{GrLeMa96, author = {Patrick Groenen and Jan de Leeuw and Rudolf Mathar}, title = "Least squares {M}ultidimensional {S}caling with transformed distances", pages = "177-185", publisher = "Springer-Verlag", series = "From Data to Knowledge: Theoretical and Practical Aspects of Classification, Data Analysis and Knowledge Organization", editor = "W. Gaul, D. Pfeifer", address = "Berlin", year = 1996, hsb = RWTH-CONV-223632, }