Set-theoretic reduced-rank adaptive filtering by adaptive projected subgradient method

Masahiro Yukawa, Rodrigo C. De Lamare, Isao Yamada

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we propose a novel reduced-rank adaptive filtering algorithm based on set-theoretic adaptive filtering. We discuss the orthonormality of the transformation (rank-reduction) matrix. We present, under the assumption that the transformation matrix has an orthonormal structure, an interpretation of the proposed algorithm in the original (fullsize) vector space. The interpretation suggests that the use of an orthonormal transformation matrix leads to performance depending solely on the subspace spanned by the column vectors of the matrix but not on the matrix itself. This is verified by simulations, and the numerical examples demonstrate the efficacy of the proposed algorithm.

Original languageEnglish
Title of host publicationConference Record - Asilomar Conference on Signals, Systems and Computers
Pages422-426
Number of pages5
DOIs
Publication statusPublished - 2007
Externally publishedYes
Event41st Asilomar Conference on Signals, Systems and Computers, ACSSC - Pacific Grove, CA, United States
Duration: 2007 Nov 42007 Nov 7

Other

Other41st Asilomar Conference on Signals, Systems and Computers, ACSSC
CountryUnited States
CityPacific Grove, CA
Period07/11/407/11/7

Fingerprint

Adaptive filtering
Vector spaces

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Yukawa, M., De Lamare, R. C., & Yamada, I. (2007). Set-theoretic reduced-rank adaptive filtering by adaptive projected subgradient method. In Conference Record - Asilomar Conference on Signals, Systems and Computers (pp. 422-426). [4487244] https://doi.org/10.1109/ACSSC.2007.4487244

Set-theoretic reduced-rank adaptive filtering by adaptive projected subgradient method. / Yukawa, Masahiro; De Lamare, Rodrigo C.; Yamada, Isao.

Conference Record - Asilomar Conference on Signals, Systems and Computers. 2007. p. 422-426 4487244.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yukawa, M, De Lamare, RC & Yamada, I 2007, Set-theoretic reduced-rank adaptive filtering by adaptive projected subgradient method. in Conference Record - Asilomar Conference on Signals, Systems and Computers., 4487244, pp. 422-426, 41st Asilomar Conference on Signals, Systems and Computers, ACSSC, Pacific Grove, CA, United States, 07/11/4. https://doi.org/10.1109/ACSSC.2007.4487244
Yukawa M, De Lamare RC, Yamada I. Set-theoretic reduced-rank adaptive filtering by adaptive projected subgradient method. In Conference Record - Asilomar Conference on Signals, Systems and Computers. 2007. p. 422-426. 4487244 https://doi.org/10.1109/ACSSC.2007.4487244
Yukawa, Masahiro ; De Lamare, Rodrigo C. ; Yamada, Isao. / Set-theoretic reduced-rank adaptive filtering by adaptive projected subgradient method. Conference Record - Asilomar Conference on Signals, Systems and Computers. 2007. pp. 422-426
@inproceedings{5c72a96aa5ba444c84350f958e4c9a0a,
title = "Set-theoretic reduced-rank adaptive filtering by adaptive projected subgradient method",
abstract = "In this paper, we propose a novel reduced-rank adaptive filtering algorithm based on set-theoretic adaptive filtering. We discuss the orthonormality of the transformation (rank-reduction) matrix. We present, under the assumption that the transformation matrix has an orthonormal structure, an interpretation of the proposed algorithm in the original (fullsize) vector space. The interpretation suggests that the use of an orthonormal transformation matrix leads to performance depending solely on the subspace spanned by the column vectors of the matrix but not on the matrix itself. This is verified by simulations, and the numerical examples demonstrate the efficacy of the proposed algorithm.",
author = "Masahiro Yukawa and {De Lamare}, {Rodrigo C.} and Isao Yamada",
year = "2007",
doi = "10.1109/ACSSC.2007.4487244",
language = "English",
isbn = "9781424421107",
pages = "422--426",
booktitle = "Conference Record - Asilomar Conference on Signals, Systems and Computers",

}

TY - GEN

T1 - Set-theoretic reduced-rank adaptive filtering by adaptive projected subgradient method

AU - Yukawa, Masahiro

AU - De Lamare, Rodrigo C.

AU - Yamada, Isao

PY - 2007

Y1 - 2007

N2 - In this paper, we propose a novel reduced-rank adaptive filtering algorithm based on set-theoretic adaptive filtering. We discuss the orthonormality of the transformation (rank-reduction) matrix. We present, under the assumption that the transformation matrix has an orthonormal structure, an interpretation of the proposed algorithm in the original (fullsize) vector space. The interpretation suggests that the use of an orthonormal transformation matrix leads to performance depending solely on the subspace spanned by the column vectors of the matrix but not on the matrix itself. This is verified by simulations, and the numerical examples demonstrate the efficacy of the proposed algorithm.

AB - In this paper, we propose a novel reduced-rank adaptive filtering algorithm based on set-theoretic adaptive filtering. We discuss the orthonormality of the transformation (rank-reduction) matrix. We present, under the assumption that the transformation matrix has an orthonormal structure, an interpretation of the proposed algorithm in the original (fullsize) vector space. The interpretation suggests that the use of an orthonormal transformation matrix leads to performance depending solely on the subspace spanned by the column vectors of the matrix but not on the matrix itself. This is verified by simulations, and the numerical examples demonstrate the efficacy of the proposed algorithm.

UR - http://www.scopus.com/inward/record.url?scp=50249103899&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50249103899&partnerID=8YFLogxK

U2 - 10.1109/ACSSC.2007.4487244

DO - 10.1109/ACSSC.2007.4487244

M3 - Conference contribution

AN - SCOPUS:50249103899

SN - 9781424421107

SP - 422

EP - 426

BT - Conference Record - Asilomar Conference on Signals, Systems and Computers

ER -