IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v66y2017i1d10.1007_s10589-016-9858-5.html
   My bibliography  Save this article

Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

Author

Listed:
  • Chao Ding

    (Chinese Academy of Sciences)

  • Hou-Duo Qi

    (The University of Southampton)

Abstract

One of the challenging problems in collaborative position localization arises when the distance measurements contain non-line-of-sight (NLOS) biases. Convex optimization has played a major role in modelling such problems and numerical algorithm developments. One of the successful examples is the semi-definite programming (SDP), which translates Euclidean distances into the constraints of positive semidefinite matrices, leading to a large number of constraints in the case of NLOS biases. In this paper, we propose a new convex optimization model that is built upon the concept of Euclidean distance matrix (EDM). The resulting EDM optimization has an advantage that its Lagrangian dual problem is well structured and hence is conducive to algorithm developments. We apply a recently proposed 3-block alternating direction method of multipliers to the dual problem and tested the algorithm on some real as well as simulated data of large scale. In particular, the EDM model significantly outperforms the existing SDP model and several others.

Suggested Citation

  • Chao Ding & Hou-Duo Qi, 2017. "Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation," Computational Optimization and Applications, Springer, vol. 66(1), pages 187-218, January.
  • Handle: RePEc:spr:coopap:v:66:y:2017:i:1:d:10.1007_s10589-016-9858-5
    DOI: 10.1007/s10589-016-9858-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-016-9858-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10589-016-9858-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gale Young & A. Householder, 1938. "Discussion of a set of points in terms of their mutual distances," Psychometrika, Springer;The Psychometric Society, vol. 3(1), pages 19-22, March.
    2. Ting Pong, 2012. "Edge-based semidefinite programming relaxation of sensor network localization with lower bound constraints," Computational Optimization and Applications, Springer, vol. 53(1), pages 23-44, September.
    3. Norbert Gaffke & Rudolf Mathar, 1989. "A cyclic projection algorithm via duality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 29-54, December.
    4. João Gouveia & Ting Pong, 2012. "Comparing SOS and SDP relaxations of sensor network localization," Computational Optimization and Applications, Springer, vol. 52(3), pages 609-627, July.
    5. Jiawang Nie, 2009. "Sum of squares method for sensor network localization," Computational Optimization and Applications, Springer, vol. 43(2), pages 151-179, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fengzhen Zhai & Qingna Li, 2020. "A Euclidean distance matrix model for protein molecular conformation," Journal of Global Optimization, Springer, vol. 76(4), pages 709-728, April.
    2. Qian Zhang & Xinyuan Zhao & Chao Ding, 2021. "Matrix optimization based Euclidean embedding with outliers," Computational Optimization and Applications, Springer, vol. 79(2), pages 235-271, June.
    3. Panpan Yu & Qingna Li, 2018. "Ordinal Distance Metric Learning with MDS for Image Ranking," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-19, February.
    4. Si-Tong Lu & Miao Zhang & Qing-Na Li, 2020. "Feasibility and a fast algorithm for Euclidean distance matrix optimization with ordinal constraints," Computational Optimization and Applications, Springer, vol. 76(2), pages 535-569, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kuroda, Kaori & Hashiguchi, Hiroki & Fujiwara, Kantaro & Ikeguchi, Tohru, 2014. "Reconstruction of network structures from marked point processes using multi-dimensional scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 194-204.
    2. Fengzhen Zhai & Qingna Li, 2020. "A Euclidean distance matrix model for protein molecular conformation," Journal of Global Optimization, Springer, vol. 76(4), pages 709-728, April.
    3. F. Deutsch & W. Li & J. Swetits, 1999. "Fenchel Duality and the Strong Conical Hull Intersection Property," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 681-695, September.
    4. François Bavaud, 2011. "On the Schoenberg Transformations in Data Analysis: Theory and Illustrations," Journal of Classification, Springer;The Classification Society, vol. 28(3), pages 297-314, October.
    5. Meng-Meng Zheng & Zheng-Hai Huang & Sheng-Long Hu, 2022. "Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space," Journal of Global Optimization, Springer, vol. 84(2), pages 415-440, October.
    6. W. Alan Nicewander & Joseph Lee Rodgers, 2022. "Obituary: Bruce McArthur Bloxom 1938–2020," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1042-1044, September.
    7. Panpan Yu & Qingna Li, 2018. "Ordinal Distance Metric Learning with MDS for Image Ranking," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-19, February.
    8. Groenen, P.J.F. & van der Lans, A., 2006. "Multidimensional Scaling with Regional Restrictions for Facet Theory: An Application to Levi's Political Protest Data," ERIM Report Series Research in Management ERS-2006-057-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    9. Zha, Hongyuan & Zhang, Zhenyue, 2007. "Continuum Isomap for manifold learnings," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 184-200, September.
    10. Cornelius Fritz & Göran Kauermann, 2022. "On the interplay of regional mobility, social connectedness and the spread of COVID‐19 in Germany," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 400-424, January.
    11. Maarten M. Kampert & Jacqueline J. Meulman & Jerome H. Friedman, 2017. "rCOSA: A Software Package for Clustering Objects on Subsets of Attributes," Journal of Classification, Springer;The Classification Society, vol. 34(3), pages 514-547, October.
    12. 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.
    13. Luwan Zhang & Grace Wahba & Ming Yuan, 2016. "Distance shrinkage and Euclidean embedding via regularized kernel estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 849-867, September.
    14. Si-Tong Lu & Miao Zhang & Qing-Na Li, 2020. "Feasibility and a fast algorithm for Euclidean distance matrix optimization with ordinal constraints," Computational Optimization and Applications, Springer, vol. 76(2), pages 535-569, June.
    15. Alberto Santini & Michael Schneider & Thibaut Vidal & Daniele Vigo, 2023. "Decomposition Strategies for Vehicle Routing Heuristics," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 543-559, May.
    16. J. Carroll, 1985. "Review," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 133-140, March.
    17. Frank de Meijer & Renata Sotirov, 2021. "SDP-Based Bounds for the Quadratic Cycle Cover Problem via Cutting-Plane Augmented Lagrangian Methods and Reinforcement Learning," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1262-1276, October.
    18. Chin How Jeffrey Pang, 2019. "Dykstra’s Splitting and an Approximate Proximal Point Algorithm for Minimizing the Sum of Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1019-1049, September.
    19. Gnot, Stanislaw & Grzadziel, Mariusz, 2002. "Nonnegative Minimum Biased Quadratic Estimation in Mixed Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 217-233, February.
    20. Kristijan Cafuta, 2019. "Sums of Hermitian squares decomposition of non-commutative polynomials in non-symmetric variables using NCSOStools," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 397-413, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:66:y:2017:i:1:d:10.1007_s10589-016-9858-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.