Projected Kernel Least Mean p-Power Algorithm: Convergence Analyses and Modifications

Zhao, J; Zhang, H; Wang, G; Zhang, JA

Projected Kernel Least Mean p-Power Algorithm: Convergence Analyses and Modifications

Zhao, J Zhang, H Wang, G Zhang, JA

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Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Transactions on Circuits and Systems I: Regular Papers, 2020, 67, (10), pp. 3498-3511
Issue Date:: 2020-10-01

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Field	Value	Language
dc.contributor.author	Zhao, J
dc.contributor.author	Zhang, H
dc.contributor.author	Wang, G
dc.contributor.author	Zhang, JA
dc.date.accessioned	2021-02-21T09:46:17Z
dc.date.available	2021-02-21T09:46:17Z
dc.date.issued	2020-10-01
dc.identifier.citation	IEEE Transactions on Circuits and Systems I: Regular Papers, 2020, 67, (10), pp. 3498-3511
dc.identifier.issn	1549-8328
dc.identifier.issn	1558-0806
dc.identifier.uri	http://hdl.handle.net/10453/146247
dc.description.abstract	© 2004-2012 IEEE. Sparsified kernel adaptive filters (SKAFs) is an attractive filtering solution with low memory and computational complexity. Most of existing SKAFs are based on the mean square error (MSE) criterion under Gaussian noise assumption for its simplicity and convenience. When the assumption deviates largely from the underlying truth, the performance of these methods could degrade significantly. In this paper, we propose a novel SKAF, named as projected kernel least mean $p$ -power algorithm (PKLMP), based on the mean $p$ -power error (MPE) criterion and vector projection (VP) method. We provide convergence analyses in terms of the stead-state MSE, based on a Taylor expansion method, and derive the lower and upper bounds for the steady-state excess MSE. We also conduct mean convergence analysis for PKLMP, and derive convergence conditions. To exploit the information in the desired outputs, we further derive a modified PKLMP by smoothing the desired signal. Finally, a simple and effective online variable kernel centers strategy is proposed to improve the filtering performance of the proposed KAFs. Simulation results under a static function estimation, a chaotic time-series prediction, and two real-world time-series predictions are conducted and validate the effectiveness of the proposed PKLMP algorithms.
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation.ispartof	IEEE Transactions on Circuits and Systems I: Regular Papers
dc.relation.isbasedon	10.1109/TCSI.2020.2993840
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.	en_US
dc.subject	0906 Electrical and Electronic Engineering
dc.subject.classification	Electrical & Electronic Engineering
dc.title	Projected Kernel Least Mean p-Power Algorithm: Convergence Analyses and Modifications
dc.type	Journal Article
utslib.citation.volume	67
utslib.for	0906 Electrical and Electronic Engineering
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - GBDTC - Global Big Data Technologies
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	/University of Technology Sydney
utslib.copyright.status	open_access	*
dc.date.updated	2021-02-21T09:46:05Z
pubs.issue	10
pubs.publication-status	Published
pubs.volume	67
utslib.citation.issue	10

Abstract:

© 2004-2012 IEEE. Sparsified kernel adaptive filters (SKAFs) is an attractive filtering solution with low memory and computational complexity. Most of existing SKAFs are based on the mean square error (MSE) criterion under Gaussian noise assumption for its simplicity and convenience. When the assumption deviates largely from the underlying truth, the performance of these methods could degrade significantly. In this paper, we propose a novel SKAF, named as projected kernel least mean $p$ -power algorithm (PKLMP), based on the mean $p$ -power error (MPE) criterion and vector projection (VP) method. We provide convergence analyses in terms of the stead-state MSE, based on a Taylor expansion method, and derive the lower and upper bounds for the steady-state excess MSE. We also conduct mean convergence analysis for PKLMP, and derive convergence conditions. To exploit the information in the desired outputs, we further derive a modified PKLMP by smoothing the desired signal. Finally, a simple and effective online variable kernel centers strategy is proposed to improve the filtering performance of the proposed KAFs. Simulation results under a static function estimation, a chaotic time-series prediction, and two real-world time-series predictions are conducted and validate the effectiveness of the proposed PKLMP algorithms.

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http://hdl.handle.net/10453/146247