Algorithms in Convex Analysis to Fit lp-Distance Matrices

R. Mathar and R. Meyer

Journal of Multivariate Analysis, 1994, vol. 51, issue 1, 102-120

Abstract: We consider the MDS problem of fitting an lp-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 [set membership, variant] [1, 2].

Date: 1994
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