Nonlinear mapping and distance geometry
| hal.structure.identifier | Pleiade, from patterns to models in computational biodiversity and biotechnology [PLEIADE] | |
| hal.structure.identifier | Biodiversité, Gènes & Communautés [BioGeCo] | |
| dc.contributor.author | FRANC, Alain | |
| hal.structure.identifier | High-End Parallel Algorithms for Challenging Numerical Simulations [HiePACS] | |
| dc.contributor.author | BLANCHARD, Pierre | |
| hal.structure.identifier | High-End Parallel Algorithms for Challenging Numerical Simulations [HiePACS] | |
| dc.contributor.author | COULAUD, Olivier | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 1862-4472 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | Distance Geometry Problem | |
| dc.subject.en | Nonlinear Mapping | |
| dc.subject.en | Least Square Scaling | |
| dc.title.en | Nonlinear mapping and distance geometry | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s11590-019-01431-y | |
| dc.subject.hal | Sciences du Vivant [q-bio] | |
| dc.subject.hal | Sciences du Vivant [q-bio]/Biodiversité | |
| dc.identifier.arxiv | 1810.08661 | |
| bordeaux.journal | Optimization Letters | |
| bordeaux.page | 453-467 | |
| bordeaux.volume | 14 | |
| bordeaux.issue | 2 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02124882 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02124882v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Optimization%20Letters&rft.date=2020&rft.volume=14&rft.issue=2&rft.spage=453-467&rft.epage=453-467&rft.eissn=1862-4472&rft.issn=1862-4472&rft.au=FRANC,%20Alain&BLANCHARD,%20Pierre&COULAUD,%20Olivier&rft.genre=article |
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