## edmcr

An R package for Euclidean (squared) distance matrix completion (and
determining point configurations based on the completed matrix.)

## Description

Implements various general algorithms to estimate missing elements of
a Euclidean (squared) distance matrix.

Includes optimization methods based on semi-definite programming,
nonparametric position, and dissimilarity parameterization formulas.

When the only non-missing distances are those on the minimal spanning
tree, the guided random search algorithm will complete the matrix while
preserving the minimal spanning tree.

Point configurations in specified dimensions can be determined from
the completions.

Special problems such as the sensor localization problem and
reconstructing the geometry of a molecular structure can also be
solved.

Online documentation: https://great-northern-diver.github.io/edmcr/

## References

- Alfakih, Khandani, and Wolkowicz (1999) “Solving Euclidean Distance
Matrix Completion Problems Via Semidefinite Programming”, Computational
Optimization and Applications, Volume 12, pages 13–30 doi:10.1023/A:1008655427845
- Trosset (2000) “Distance Matrix Completion by Numerical
Optimization”, Computational Optimization and Applications, Volume 17,
pages 11–22 doi:10.1023/A:1008722907820
- Krislock and Henry Wolkowicz (2010) “Explicit sensor network
localization using semidefinite representations and facial reductions”,
SIAM Journal on Optimization, Volume 20(5), pages 2679–2708 doi:10.1137/090759392
- Fang and O’Leary (2012) “Euclidean Matrix Completion Problems”,
Optimization Methods and Software, Volume 27, pages 695-717, doi:10.1080/10556788.2011.643888
- Rahman and Oldford (2018) “Euclidean Distance Matrix Completion and
Point Configurations from the Minimal Spanning Tree”, SIAM Journal on
Optimization, Volume 28, pages 528-550 doi:10.1137/16M1092350
- Rahman (2018) “Preserving Measured Structure During Generation and
Reduction of Multivariate Point Configurations”, Doctoral dissertation
UWSpace theses http://hdl.handle.net/10012/13365

Other source code:

- makes use of some
`C`

source code (sparse matrix column
ordering authored by Stefan I. Larimore and Timothy A. Davis) from the
Suite Sparse collection.