Pairwise Optimal Weight Realization-Acceleration Technique for Set-Theoretic Adaptive Parallel Subgradient Projection Algorithm
The adaptive parallel subgradient projection (PSP) algorithm was proposed in 2002 as a set-theoretic adaptive filtering algorithm providing fast and stable convergence, robustness against noise, and low computational complexity by using weighted parallel projections onto multiple time-varying closed...
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| Vydáno v: | IEEE transactions on signal processing Ročník 54; číslo 12; s. 4557 - 4571 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York, NY
IEEE
01.12.2006
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1053-587X, 1941-0476 |
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| Abstract | The adaptive parallel subgradient projection (PSP) algorithm was proposed in 2002 as a set-theoretic adaptive filtering algorithm providing fast and stable convergence, robustness against noise, and low computational complexity by using weighted parallel projections onto multiple time-varying closed half-spaces. In this paper, we present a novel weighting technique named pairwise optimal weight realization (POWER) for further acceleration of the adaptive PSP algorithm. A simple closed-form formula is derived to compute the projection onto the intersection of two closed half-spaces defined by a triplet of vectors. Using the formula inductively, the proposed weighting technique realizes a good direction of update. The resulting weights turn out to be pairwise optimal in a certain sense. The proposed algorithm has the inherently parallel structure composed of q primitive functions, hence its total computational complexity O(qrN) is reduced to O(rN) with q concurrent processors (r: a constant positive integer). Numerical examples demonstrate that the proposed technique for r=1 yields significantly faster convergence than not only adaptive PSP with uniform weights, affine projection algorithm, and fast Newton transversal filters but also the regularized recursive least squares algorithm |
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| AbstractList | The adaptive parallel subgradient projection (PSP) algorithm was proposed in 2002 as a set-theoretic adaptive filtering algorithm providing fast and stable convergence, robustness against noise, and low computational complexity by using weighted parallel projections onto multiple time-varying closed half-spaces. The adaptive parallel subgradient projection (PSP) algorithm was proposed in 2002 as a set-theoretic adaptive filtering algorithm providing fast and stable convergence, robustness against noise, and low computational complexity by using weighted parallel projections onto multiple time-varying closed half-spaces. In this paper, we present a novel weighting technique named pairwise optimal weight realization (POWER) for further acceleration of the adaptive PSP algorithm. A simple closed-form formula is derived to compute the projection onto the intersection of two closed half-spaces defined by a triplet of vectors. Using the formula inductively, the proposed weighting technique realizes a good direction of update. The resulting weights turn out to be pairwise optimal in a certain sense. The proposed algorithm has the inherently parallel structure composed of q primitive functions, hence its total computational complexity O(qrN) is reduced to O(rN) with q concurrent processors (r: a constant positive integer). Numerical examples demonstrate that the proposed technique for r=1 yields significantly faster convergence than not only adaptive PSP with uniform weights, affine projection algorithm, and fast Newton transversal filters but also the regularized recursive least squares algorithm |
| Author | Yamada, I. Yukawa, M. |
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| Cites_doi | 10.1109/ICASSP.1995.479482 10.1109/TASSP.1984.1164334 10.1287/moor.26.2.248.10558 10.1109/78.485923 10.1137/S0036144593251710 10.1081/NFA-200045806 10.1002/ecja.4400670503 10.1109/ACSSC.2003.1291982 10.1109/79.774932 10.1109/78.827542 10.1109/78.91175 10.1109/TASSP.1983.1164224 10.1109/78.575687 10.1109/29.31289 10.1155/ASP/2006/84797 10.1109/ICASSP.1996.543281 10.1109/97.668945 10.1109/78.995065 10.1109/ACSSC.2003.1292345 10.1016/0165-1684(89)90060-1 10.1080/00207177808922343 10.1109/97.404129 10.1109/78.80769 10.1093/ietfec/e88-a.8.2062 10.1109/78.661344 10.1109/5.214546 10.1002/eej.4390950515 10.1109/TAC.1967.1098599 10.1109/TSP.2006.881225 10.1109/ICASSP.1988.196852 10.1109/TSP.2005.851110 |
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| Keywords | Parallel algorithm optimal weight design Adaptive algorithm Adaptive filtering Parallel architectures Affine transformation Recursive algorithm Computational complexity Half space Time variation Adaptive parallel subgradient projection set-theoretic adaptive filtering Optimal design Fast filter Weighting Least squares method Transverse filter Convergence rate Noise immunity Numerical simulation Set theory Fast algorithm Newton method |
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| References | ref13 yukawa (ref35) 2004; e87 a ref34 ref12 yamada (ref31) 2003; 86 ref15 ref36 ref14 ref11 haykin (ref1) 2002 ref32 ref10 ref39 ref17 ref38 ref16 ref19 (ref2) 2003 censor (ref30) 1997 slock (ref21) 1992 (ref27) 2001 ref24 ref45 ref23 yamada (ref33) 2004 ref25 ref20 bauschke (ref42) 1996 ogura (ref41) 2005; 6 ref22 ref44 ref43 sayed (ref3) 2003 albert (ref26) 1967 ref28 luenberger (ref46) 1969 ref29 ref8 ref7 ref9 ref4 ref6 ref5 (ref18) 2000 ref40 cavalcante (ref37) 2004; e87 a |
| References_xml | – volume: 86 start-page: 654 year: 2003 ident: ref31 article-title: adaptive projected subgradient method: a unified view for projection based adaptive algorithms publication-title: J IEICE – ident: ref22 doi: 10.1109/ICASSP.1995.479482 – year: 2002 ident: ref1 publication-title: Adaptive Filter Theory – ident: ref10 doi: 10.1109/TASSP.1984.1164334 – ident: ref40 doi: 10.1287/moor.26.2.248.10558 – ident: ref7 doi: 10.1109/78.485923 – volume: e87 a start-page: 1973 year: 2004 ident: ref37 article-title: a fast blind mai reduction based on adaptive projected subgradient method publication-title: IEICE Trans Fundam – ident: ref29 doi: 10.1137/S0036144593251710 – year: 1997 ident: ref30 publication-title: Parallel Optimization Theory Algorithm and Optimization – ident: ref34 doi: 10.1081/NFA-200045806 – ident: ref20 doi: 10.1002/ecja.4400670503 – ident: ref32 doi: 10.1109/ACSSC.2003.1291982 – start-page: 639 year: 2004 ident: ref33 article-title: adaptive projected subgradient method and its acceleration techniques publication-title: Proc IFAC Workshop Adaptation and Learning in Control and Signal Processing (ALCOSP) – year: 1996 ident: ref42 publication-title: Projection algorithms and monotone operators – ident: ref11 doi: 10.1109/79.774932 – ident: ref24 doi: 10.1109/78.827542 – volume: e87 a start-page: 1949 year: 2004 ident: ref35 article-title: efficient adaptive stereo echo canceling schemes based on simultaneous use of multiple state data publication-title: IEICE Trans Fundam – ident: ref17 doi: 10.1109/78.91175 – ident: ref9 doi: 10.1109/TASSP.1983.1164224 – ident: ref43 doi: 10.1109/78.575687 – volume: 6 start-page: 187 year: 2005 ident: ref41 article-title: a deep outer approximating half space of the level set of certain quadratic functions publication-title: J Nonlinear Convex Anal – ident: ref12 doi: 10.1109/29.31289 – ident: ref36 doi: 10.1155/ASP/2006/84797 – year: 2003 ident: ref2 publication-title: Adaptive Signal ProcessingApplications to Real-World Problems – ident: ref16 doi: 10.1109/ICASSP.1996.543281 – ident: ref5 doi: 10.1109/97.668945 – ident: ref4 doi: 10.1109/78.995065 – ident: ref6 doi: 10.1109/ACSSC.2003.1292345 – ident: ref14 doi: 10.1016/0165-1684(89)90060-1 – ident: ref8 doi: 10.1080/00207177808922343 – ident: ref45 doi: 10.1109/97.404129 – ident: ref15 doi: 10.1109/78.80769 – ident: ref38 doi: 10.1093/ietfec/e88-a.8.2062 – ident: ref23 doi: 10.1109/78.661344 – year: 2000 ident: ref18 publication-title: Acoustic Signal Processing for Telecommunication – ident: ref28 doi: 10.1109/5.214546 – year: 2001 ident: ref27 publication-title: Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications – ident: ref19 doi: 10.1002/eej.4390950515 – ident: ref25 doi: 10.1109/TAC.1967.1098599 – ident: ref39 doi: 10.1109/TSP.2006.881225 – year: 1969 ident: ref46 publication-title: Optimization by vector space methods – start-page: 550 year: 1992 ident: ref21 article-title: the block underdetermined covariance (buc) fast transversal filter (ftf) algorithm for adaptive filtering publication-title: Proc Asilomar Conf Signals Syst Comput – year: 1967 ident: ref26 publication-title: Stochastic Approximation and Nonlinear Regression – ident: ref13 doi: 10.1109/ICASSP.1988.196852 – year: 2003 ident: ref3 publication-title: Fundamentals of Adaptive Filtering – ident: ref44 doi: 10.1109/TSP.2005.851110 |
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| SubjectTerms | Acceleration Adaptive algorithms Adaptive filters Adaptive parallel subgradient projection Algorithms Applied sciences Computational complexity Convergence Detection, estimation, filtering, equalization, prediction Exact sciences and technology Filtering algorithms Half spaces Information, signal and communications theory Least squares methods Mathematical analysis Mathematical models optimal weight design Optimization Projection Projection algorithms Resonance light scattering set-theoretic adaptive filtering Signal and communications theory Signal processing algorithms Signal, noise Studies Telecommunications and information theory Transversal filters |
| Title | Pairwise Optimal Weight Realization-Acceleration Technique for Set-Theoretic Adaptive Parallel Subgradient Projection Algorithm |
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