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Sparse Diffusion Least Mean-Square Algorithm with Hard Thresholding over Networks

Author

Listed:
  • Han-Sol Lee

    (System LSI Business, Samsung Electronics, Hwaseong 18448, Republic of Korea)

  • Changgyun Jin

    (Department of Applied Artificial Intelligence, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea)

  • Chanwoo Shin

    (Department of Applied Artificial Intelligence, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea)

  • Seong-Eun Kim

    (Department of Applied Artificial Intelligence, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea)

Abstract

This paper proposes a distributed estimation technique utilizing the diffusion least mean-square (LMS) algorithm, specifically designed for sparse systems in which many coefficients of the system are zeros. To efficiently utilize the sparse representation of the system and achieve a promising performance, we have incorporated L 0 -norm regularization into the diffusion LMS algorithm. This integration is accomplished by employing hard thresholding through a variable splitting method into the update equation. The efficacy of our approach is validated by comprehensive theoretical analysis, rigorously examining the mean stability as well as the transient and steady-state behaviors of the proposed algorithm. The proposed algorithm preserves the behavior of large coefficients and strongly enforces smaller coefficients toward zero through the relaxation of L 0 -norm regularization. Experimental results show that the proposed algorithm achieves superior convergence performance compared with conventional sparse algorithms.

Suggested Citation

  • Han-Sol Lee & Changgyun Jin & Chanwoo Shin & Seong-Eun Kim, 2023. "Sparse Diffusion Least Mean-Square Algorithm with Hard Thresholding over Networks," Mathematics, MDPI, vol. 11(22), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4638-:d:1279612
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    References listed on IDEAS

    as
    1. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
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