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Algorithms in Convex Analysis to Fit lp-Distance Matrices

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  • Mathar, R.
  • Meyer, R.

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].

Suggested Citation

  • Mathar, R. & Meyer, R., 1994. "Algorithms in Convex Analysis to Fit lp-Distance Matrices," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 102-120, October.
    • Handle: RePEc:eee:jmvana:v:51:y:1994:i:1:p:102-120
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