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

Han-Sol Lee, Changgyun Jin, Chanwoo Shin and Seong-Eun Kim ()
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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

Mathematics, 2023, vol. 11, issue 22, 1-16

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.

Keywords: diffusion least mean square; distributed estimation; sparse parameter; system identification; hard thresholding (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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