Literature DB >> 18621694

A remark on global positioning from local distances.

Amit Singer1.   

Abstract

Finding the global positioning of points in Euclidean space from a local or partial set of pairwise distances is a problem in geometry that emerges naturally in sensor networks and NMR spectroscopy of proteins. We observe that the eigenvectors of a certain sparse matrix exactly match the sought coordinates. This translates to a simple and efficient algorithm that is robust to noisy distance data.

Mesh：

Year:  2008        PMID： 18621694      PMCID： PMC2474529          DOI： 10.1073/pnas.0709842104

Source DB:  PubMed          Journal:  Proc Natl Acad Sci U S A        ISSN： 0027-8424            Impact factor:   11.205


  4 in total

1.  Nonlinear dimensionality reduction by locally linear embedding.

Authors:  S T Roweis; L K Saul
Journal:  Science       Date:  2000-12-22       Impact factor: 47.728

2.  Framework for kernel regularization with application to protein clustering.

Authors:  Fan Lu; Sündüz Keles; Stephen J Wright; Grace Wahba
Journal:  Proc Natl Acad Sci U S A       Date:  2005-08-18       Impact factor: 11.205

3.  Hessian eigenmaps: locally linear embedding techniques for high-dimensional data.

Authors:  David L Donoho; Carrie Grimes
Journal:  Proc Natl Acad Sci U S A       Date:  2003-04-30       Impact factor: 11.205

4.  Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps.

Authors:  R R Coifman; S Lafon; A B Lee; M Maggioni; B Nadler; F Warner; S W Zucker
Journal:  Proc Natl Acad Sci U S A       Date:  2005-05-17       Impact factor: 12.779
  4 in total
  8 in total

1.  Reference Free Structure Determination through Eigenvectors of Center of Mass Operators.

Authors:  Ronald R Coifman; Yoel Shkolnisky; Fred J Sigworth; Amit Singer
Journal:  Appl Comput Harmon Anal       Date:  2010-05       Impact factor: 3.055

2.  DNA Microscopy: Optics-free Spatio-genetic Imaging by a Stand-Alone Chemical Reaction.

Authors:  Joshua A Weinstein; Aviv Regev; Feng Zhang
Journal:  Cell       Date:  2019-06-20       Impact factor: 41.582

3.  Angular Synchronization by Eigenvectors and Semidefinite Programming.

Authors:  A Singer
Journal:  Appl Comput Harmon Anal       Date:  2011-01-30       Impact factor: 3.055

4.  Eigenvector synchronization, graph rigidity and the molecule problem.

Authors:  Mihai Cucuringu; Amit Singer; David Cowburn
Journal:  Inf inference       Date:  2012-12

5.  Sensor Network Localization by Eigenvector Synchronization Over the Euclidean Group.

Authors:  Mihai Cucuringu; Yaron Lipman; Amit Singer
Journal:  ACM Trans Sens Netw       Date:  2012-07       Impact factor: 2.253

6.  Global geometric affinity for revealing high fidelity protein interaction network.

Authors:  Yi Fang; William Benjamin; Mengtian Sun; Karthik Ramani
Journal:  PLoS One       Date:  2011-05-03       Impact factor: 3.240

7.  Heat-passing framework for robust interpretation of data in networks.

Authors:  Yi Fang; Mengtian Sun; Karthik Ramani
Journal:  PLoS One       Date:  2015-02-10       Impact factor: 3.240

8.  Spectroscopic stimulated Raman scattering imaging of highly dynamic specimens through matrix completion.

Authors:  Haonan Lin; Chien-Sheng Liao; Pu Wang; Nan Kong; Ji-Xin Cheng
Journal:  Light Sci Appl       Date:  2018-05-04       Impact factor: 17.782
  8 in total

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