Nonlinear mapping and distance geometry
FRANC, Alain
Pleiade, from patterns to models in computational biodiversity and biotechnology [PLEIADE]
Biodiversité, Gènes & Communautés [BioGeCo]
Pleiade, from patterns to models in computational biodiversity and biotechnology [PLEIADE]
Biodiversité, Gènes & Communautés [BioGeCo]
FRANC, Alain
Pleiade, from patterns to models in computational biodiversity and biotechnology [PLEIADE]
Biodiversité, Gènes & Communautés [BioGeCo]
< Leer menos
Pleiade, from patterns to models in computational biodiversity and biotechnology [PLEIADE]
Biodiversité, Gènes & Communautés [BioGeCo]
Idioma
en
Article de revue
Este ítem está publicado en
Optimization Letters. 2020, vol. 14, n° 2, p. 453-467
Springer Verlag
Resumen en inglés
Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: DGP is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear Mapping ...Leer más >
Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: DGP 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.< Leer menos
Palabras clave en inglés
Distance Geometry Problem
Nonlinear Mapping
Least Square Scaling
Orígen
Importado de HalCentros de investigación