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.
Original language | English (US) |
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Pages (from-to) | 9507-9511 |
Number of pages | 5 |
Journal | Proceedings of the National Academy of Sciences of the United States of America |
Volume | 105 |
Issue number | 28 |
DOIs | |
State | Published - Jul 15 2008 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General
Keywords
- Distance geometry
- Eigenvectors
- Multidimensional scaling
- Sensor networks