Recursive regularisation parameter selection for sparse RLS algorithm
In this Letter, the authors propose a recursive regularisation parameter selection method for sparse recursive least squares (RLS) algorithm. The proposed RLS algorithm is regularised by a convex function, which equals the linear combination of two convex functions, one to cope with random sparsity,...
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| Veröffentlicht in: | Electronics letters Jg. 54; H. 5; S. 286 - 287 |
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The Institution of Engineering and Technology
08.03.2018
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| ISSN: | 0013-5194, 1350-911X, 1350-911X |
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| Abstract | In this Letter, the authors propose a recursive regularisation parameter selection method for sparse recursive least squares (RLS) algorithm. The proposed RLS algorithm is regularised by a convex function, which equals the linear combination of two convex functions, one to cope with random sparsity, and the other to cope with group sparsity. The normal equations corresponding to the RLS algorithm with the proposed convex regularised penalty function are derived, and a recursive algorithm to update the regularisation parameters (i.e. the coefficients of the linear combination) is proposed. As an example, by using the linear combination of an $l_0$l0-norm and an $l_{2\comma 0}$l2,0-norm as the penalty function, simulation results show that the proposed sparse RLS with recursive regularisation parameter selection can achieve better performance in terms of mean square error for a slowly time-varying sparse system with both random sparsity and group sparsity. |
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| AbstractList | In this Letter, the authors propose a recursive regularisation parameter selection method for sparse recursive least squares (RLS) algorithm. The proposed RLS algorithm is regularised by a convex function, which equals the linear combination of two convex functions, one to cope with random sparsity, and the other to cope with group sparsity. The normal equations corresponding to the RLS algorithm with the proposed convex regularised penalty function are derived, and a recursive algorithm to update the regularisation parameters (i.e. the coefficients of the linear combination) is proposed. As an example, by using the linear combination of an $l_0$l0-norm and an $l_{2\comma 0}$l2,0-norm as the penalty function, simulation results show that the proposed sparse RLS with recursive regularisation parameter selection can achieve better performance in terms of mean square error for a slowly time-varying sparse system with both random sparsity and group sparsity. In this Letter, the authors propose a recursive regularisation parameter selection method for sparse recursive least squares (RLS) algorithm. The proposed RLS algorithm is regularised by a convex function, which equals the linear combination of two convex functions, one to cope with random sparsity, and the other to cope with group sparsity. The normal equations corresponding to the RLS algorithm with the proposed convex regularised penalty function are derived, and a recursive algorithm to update the regularisation parameters (i.e. the coefficients of the linear combination) is proposed. As an example, by using the linear combination of an ‐norm and an ‐norm as the penalty function, simulation results show that the proposed sparse RLS with recursive regularisation parameter selection can achieve better performance in terms of mean square error for a slowly time‐varying sparse system with both random sparsity and group sparsity. In this Letter, the authors propose a recursive regularisation parameter selection method for sparse recursive least squares (RLS) algorithm. The proposed RLS algorithm is regularised by a convex function, which equals the linear combination of two convex functions, one to cope with random sparsity, and the other to cope with group sparsity. The normal equations corresponding to the RLS algorithm with the proposed convex regularised penalty function are derived, and a recursive algorithm to update the regularisation parameters (i.e. the coefficients of the linear combination) is proposed. As an example, by using the linear combination of an l0‐norm and an l2,0‐norm as the penalty function, simulation results show that the proposed sparse RLS with recursive regularisation parameter selection can achieve better performance in terms of mean square error for a slowly time‐varying sparse system with both random sparsity and group sparsity. |
| Author | Zhang, Youwen Sun, Dajun Liu, Lu |
| Author_xml | – sequence: 1 givenname: Dajun surname: Sun fullname: Sun, Dajun organization: College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, People's Republic of China – sequence: 2 givenname: Lu surname: Liu fullname: Liu, Lu email: liulu_uwa@hrbeu.edu.cn organization: College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, People's Republic of China – sequence: 3 givenname: Youwen surname: Zhang fullname: Zhang, Youwen organization: College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, People's Republic of China |
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| Cites_doi | 10.1016/j.sigpro.2011.02.013 10.1109/LSP.2011.2159373 10.1049/el.2012.3590 10.1109/TSP.2010.2046897 10.1109/TSP.2013.2258340 10.1109/TSP.2012.2192924 10.1109/TSP.2010.2048103 10.1109/TSP.2002.800414 10.1109/TASL.2008.2010156 10.1002/acs.2449 |
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| Keywords | sparse recursive least squares algorithm adaptive filters least squares approximations l0-norm adaptive filtering recursive regularisation parameter selection method random sparsity sparse RLS algorithm l2,0-norm group sparsity convex regularised penalty function time-varying sparse system |
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| SubjectTerms | adaptive filtering adaptive filters Circuits and systems convex regularised penalty function group sparsity l0‐norm l2,0‐norm least squares approximations random sparsity recursive regularisation parameter selection method sparse recursive least squares algorithm sparse RLS algorithm time‐varying sparse system |
| Title | Recursive regularisation parameter selection for sparse RLS algorithm |
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