Proportionate Adaptive Graph Signal Recovery

• Published in: IEEE transactions on signal and information processing over networks Vol. 9; pp. 386 - 396
• Main Authors: Torkamani, Razieh, Zayyani, Hadi, Korki, Mehdi
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: adaptive; Adaptive algorithms; Algorithms; Convergence; Covariance matrices; Fourier transforms; Graph signal recovery; Heuristic algorithms; Laplace equations; laplacian matrix; Least mean squares; Least mean squares algorithm; proportionate; Recovery; Signal processing; Signal processing algorithms; Signal reconstruction; Stability analysis; Symmetric matrices
• ISSN: 2373-776X; 2373-7778
• DOI: 10.1109/TSIPN.2023.3277591

This paper generalizes the proportionate-type adaptive algorithm to the graph signal processing and proposes two proportionate-type adaptive graph signal recovery algorithms. The gain matrix of the proportionate algorithm leads to faster convergence than least mean squares (LMS) algorithm. In this paper, the gain matrix is obtained in a closed-form by minimizing the gradient of the mean-square deviation (GMSD). The first algorithm is the proportionate-type graph LMS (Pt-GLMS) algorithm which simply uses a gain matrix in the recursion process of the LMS algorithm and accelerates the convergence of the Pt-GLMS algorithm compared to the LMS algorithm. The second algorithm is the proportionate-type graph extended LMS (Pt-GELMS) algorithm, which uses the previous signal vectors alongside the signal of the current iteration. The Pt-GELMS algorithm utilizes two gain matrices to control the effect of the signal of the previous iterations. The stability analyses of the algorithms are also provided. Simulation results demonstrate the efficacy of the two proposed proportionate-type LMS algorithms.