Institute for Theoretical Information Technology

Algorithms in convex analysis to fit l_p-distance matrices

Authors

R. Mathar, R. Meyer,

Abstract

        We consider the MDS problem of fitting an l_p-distance matrix to a given dissimilarity matrix with respect to the weighted least squares loss function (STRESS). The problem is reduced to the maximization of a ratio of two norms on a finite dimensional Hilbert space. A necessary condition for a point where a local maximum is attained constitutes a nonlinear eigenproblem in terms of subgradients. Explicit expressions for the subgradients of both norms are derived, a new iterative procedure for solving the nonlinear eigenproblem is proposed, and its global convergence is proved for p in [1,2].

BibT_EX Reference Entry 

@article{MaMe94,
	author = {Rudolf Mathar and Renate Meyer},
	title = "Algorithms in convex analysis to fit {$l\sb p$}-distance matrices",
	pages = "102-120",
	journal = "Journal of Multivariate Analysis",
	volume = "51",
	year = 1994,
	hsb = RWTH-CONV-223133,
	}

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