Algorithms in Convex Analysis to Fit lp-Distance Matrices
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].
Year of publication: |
1994
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Authors: | Mathar, R. ; Meyer, R. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 51.1994, 1, p. 102-120
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Publisher: |
Elsevier |
Saved in:
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