An efficient kernel normalized least mean square algorithm with compactly supported kernel

Osamu Toda; Masahiro Yukawa

doi:10.1109/ICASSP.2015.7178595

An efficient kernel normalized least mean square algorithm with compactly supported kernel

Osamu Toda, Masahiro Yukawa

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

We investigate the use of compactly supported kernels (CSKs) for the kernel normalized least mean square (KNLMS) algorithm proposed initially by Richard et al. in 2009. The use of CSKs yields sparse kernelized input vectors, offering an opportunity for complexity reduction. We propose a simple two-step method to compute the kernelized input vectors efficiently. In the first step, it computes an over-estimation of the support of the kernelized input vector based on a certain ℓ₁-ball. In the second step, it identifies the exact support by detailed examinations based on an ℓ₂-ball. Also, we employ the identified support given by the second step for coherence construction. The proposed method reduces the amount of ℓ₂-distance evaluations, leading to the complexity reduction. The numerical examples show that the proposed algorithm achieves significant complexity reduction.

Original language	English
Title of host publication	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3367-3371
Number of pages	5
Volume	2015-August
ISBN (Print)	9781467369978
DOIs	https://doi.org/10.1109/ICASSP.2015.7178595
Publication status	Published - 2015 Aug 4
Event	40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia Duration: 2014 Apr 19 → 2014 Apr 24

Other

Other	40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
Country	Australia
City	Brisbane
Period	14/4/19 → 14/4/24

Keywords

Compactly supported function
Gaussian kernel
Kernel learning
Positive definite function
Radial basis function

ASJC Scopus subject areas

Signal Processing
Software
Electrical and Electronic Engineering

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10.1109/ICASSP.2015.7178595

Cite this

An efficient kernel normalized least mean square algorithm with compactly supported kernel. / Toda, Osamu; Yukawa, Masahiro.

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. Vol. 2015-August Institute of Electrical and Electronics Engineers Inc., 2015. p. 3367-3371 7178595.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Toda, O & Yukawa, M 2015, An efficient kernel normalized least mean square algorithm with compactly supported kernel. in ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. vol. 2015-August, 7178595, Institute of Electrical and Electronics Engineers Inc., pp. 3367-3371, 40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015, Brisbane, Australia, 14/4/19. https://doi.org/10.1109/ICASSP.2015.7178595

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abstract = "We investigate the use of compactly supported kernels (CSKs) for the kernel normalized least mean square (KNLMS) algorithm proposed initially by Richard et al. in 2009. The use of CSKs yields sparse kernelized input vectors, offering an opportunity for complexity reduction. We propose a simple two-step method to compute the kernelized input vectors efficiently. In the first step, it computes an over-estimation of the support of the kernelized input vector based on a certain ℓ1-ball. In the second step, it identifies the exact support by detailed examinations based on an ℓ2-ball. Also, we employ the identified support given by the second step for coherence construction. The proposed method reduces the amount of ℓ2-distance evaluations, leading to the complexity reduction. The numerical examples show that the proposed algorithm achieves significant complexity reduction.",

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AB - We investigate the use of compactly supported kernels (CSKs) for the kernel normalized least mean square (KNLMS) algorithm proposed initially by Richard et al. in 2009. The use of CSKs yields sparse kernelized input vectors, offering an opportunity for complexity reduction. We propose a simple two-step method to compute the kernelized input vectors efficiently. In the first step, it computes an over-estimation of the support of the kernelized input vector based on a certain ℓ1-ball. In the second step, it identifies the exact support by detailed examinations based on an ℓ2-ball. Also, we employ the identified support given by the second step for coherence construction. The proposed method reduces the amount of ℓ2-distance evaluations, leading to the complexity reduction. The numerical examples show that the proposed algorithm achieves significant complexity reduction.

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An efficient kernel normalized least mean square algorithm with compactly supported kernel

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