Algorithms in Convex Analysis to Fit lp-Distance Matrices

✍ Scribed by R. Mathar; R. Meyer

• Book ID: 102973349
• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 695 KB
• Volume: 51
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1994.1052

✦ Synopsis

We consider the MDS problem of fitting an (l_{r})-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]). "'i' 1994 Academic Press. Inc.