ALGORITHMS IN CONVEX-ANALYSIS TO FIT L(P)-DISTANCE MATRICES

[摘要] 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 is an element of [I, 2]. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-01

[关键词] MULTIDIMENSIONAL SCALING;L(P)-NORM;CONSTRAINED MAXIMIZATION OF CONVEX FUNCTIONS;SUBGRADIENTS;NONLINEAR EIGENPROBLEM;INVERSE ITERATION