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Euclidean Distance Matrices and Applications

In: Handbook on Semidefinite, Conic and Polynomial Optimization

Author

Listed:
  • Nathan Krislock

    (University of Waterloo)

  • Henry Wolkowicz

    (University of Waterloo)

Abstract

Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especially the problem of wireless sensor network localization, have all become very active areas of research. The second reason for this increased interest is the close connection between EDMs and semidefinite matrices. Our recent ability to solve semidefinite programs efficiently means we can now also solve many problems involving EDMs efficiently. This chapter connects the classical approaches for EDMs with the more recent tools from semidefinite programming. We emphasize the application to sensor network localization.

Suggested Citation

  • Nathan Krislock & Henry Wolkowicz, 2012. "Euclidean Distance Matrices and Applications," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 879-914, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-0769-0_30
    DOI: 10.1007/978-1-4614-0769-0_30
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    Cited by:

    1. Xin Shen & John E. Mitchell, 2018. "A penalty method for rank minimization problems in symmetric matrices," Computational Optimization and Applications, Springer, vol. 71(2), pages 353-380, November.
    2. Marcin Bukowski & Janusz Majewski & Agnieszka Sobolewska, 2023. "The Environmental Impact of Changes in the Structure of Electricity Sources in Europe," Energies, MDPI, vol. 16(1), pages 1-22, January.
    3. Varvitsiotis, A., 2013. "Combinatorial conditions for low rank solutions in semidefinite programming," Other publications TiSEM d0fcc572-daaf-4bd9-95db-1, Tilburg University, School of Economics and Management.
    4. Nathanaël Randriamihamison & Nathalie Vialaneix & Pierre Neuvial, 2021. "Applicability and Interpretability of Ward’s Hierarchical Agglomerative Clustering With or Without Contiguity Constraints," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 363-389, July.

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