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Enhancing multidimensional scaling through a distributed algorithm

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Abstract

Classic multidimensional scaling (MDS) and scaling by majorizing a complex function (SMACOF) are well-known centralized algorithms that are used to solve MDS problem. In this paper, we present a distributed algorithm for solving MDS problem. Estimations of coordinates are performed concurrently under the assumption that each item knows only its own position and its distances from its neighbors and their approximated present locations. The update process is done by calculating the average of the current coordinate of each object and its projections on the solution spaces allocated to it by its neighbors. We apply the method to the problem of sensor localization and obtain numerical results that demonstrate the efficacy of our suggested strategy.

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Authors and Affiliations

  1. Department of Mathematics, Shahed University, P.O. Box: 18151-159, Tehran, Iran

    Zahra Gachkooban & Rahim Alizadeh

  2. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran

    Fatemeh Shakeri

Authors
  1. Zahra Gachkooban
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  2. Rahim Alizadeh
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  3. Fatemeh Shakeri
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Contributions

R. A. Investigation, Project administration, Supervision, Methodology. Z. G. Methodology, Writing-Original draft preparation, Writing- Reviewing and Editing, Programming, Visualization, Validation. F. Sh. Formal analysis, programming, Visualization.

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Correspondence to Rahim Alizadeh.

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Gachkooban, Z., Alizadeh, R. & Shakeri, F. Enhancing multidimensional scaling through a distributed algorithm. J Supercomput 80, 22049–22068 (2024). https://doi.org/10.1007/s11227-024-06302-7

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