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Nonlinear Mapping and Distance Geometry. (arXiv:1810.08661v1 [cs.CG])
来源于:arXiv
Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well
established questions: Distance Geometry Problem is about finding a Euclidean
realization of an incomplete set of distances in a Euclidean space, whereas
Nonlinear Mapping is a weighted Least Square Scaling (LSS) method. We show how
all these methods (LSS, NLM, DGP) can be assembled in a common framework, being
each identified as an instance of an optimization problem with a choice of a
weight matrix. We study the continuity between the solutions (which are point
clouds) when the weight matrix varies, and the compactness of the set of
solutions (after centering). We finally study a numerical example, showing that
solving the optimization problem is far from being simple and that the
numerical solution for a given procedure may be trapped in a local minimum. 查看全文>>