Least squares multidimensional scaling with transformed distances

Authors

P. Groenen, J. d. Leeuw, R. Mathar,

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,
	}

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