Institute for Theoretical Information Technology

Multidimensional scaling with l_p-distances, a unifying approach

Authors

R. Mathar,

Abstract

        In a unifying approach, this note deals with three different methods to find the best embedding of n objects in an l_p-space, p>=1, if only pairwise dissimilarities are given and fitting is measured by weighted least squares. The procedures are based on (1) a nested algorithm with an inner linear constrained problem, (2) a generalized eigenvector procedure resembling inverse iteration, and (3) majorization. All resulting algorithms are quite similar, though the optimization problem is approached from different viewpoints. This paper explains why, by interpreting (2) and (3) as a relaxed version of a first order subgradient method.

BibT_EX Reference Entry 

@inbook{Ma94,
	author = {Rudolf Mathar},
	title = "{M}ultidimensional {S}caling with {$l\sb p$}-distances, a unifying approach",
	pages = "325-331",
	publisher = "Springer-Verlag",
	series = "Information Systems and Data Analysis",
	editor = "H.H. Bock, W. Lenski, M.M. Richter",
	address = "Heidelberg",
	year = 1994,
	hsb = RWTH-CONV-223630,
	}

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