The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
본 논문에서는 선형 관련 일반화-모로-강화(LiGME) 모델을 위한 일반화 모로 향상 행렬(GME 행렬)의 통합 대수 설계를 제안합니다. LiGME 모델은 희소성(또는 낮은 순위) 인식 추정을 위한 선형 관련 비볼록 정규화 도구를 구성하기 위한 프레임워크로 확립되었습니다. 여기서 GME 행렬의 설계는 모델의 전체 볼록성을 보장하는 핵심입니다. 제안된 설계는 LiGME 모델의 정규화에 관련된 일반 선형 연산자에 적용 가능하며 고유 분해 또는 반복 계산이 필요하지 않습니다. 또한 제안된 GME 행렬을 사용하여 그룹 희소성 인식 최소 제곱 추정 문제에 LiGME 모델을 적용하는 방법도 제시합니다. 수치 실험은 LiGME 모델에서 제안된 GME 매트릭스의 효율성을 보여줍니다.
Yang CHEN
Tokyo Institute of Technology
Masao YAMAGISHI
Tokyo Institute of Technology
Isao YAMADA
Tokyo Institute of Technology
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부
Yang CHEN, Masao YAMAGISHI, Isao YAMADA, "A Unified Design of Generalized Moreau Enhancement Matrix for Sparsity Aware LiGME Models" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 8, pp. 1025-1036, August 2023, doi: 10.1587/transfun.2022EAP1118.
Abstract: In this paper, we propose a unified algebraic design of the generalized Moreau enhancement matrix (GME matrix) for the Linearly involved Generalized-Moreau-Enhanced (LiGME) model. The LiGME model has been established as a framework to construct linearly involved nonconvex regularizers for sparsity (or low-rank) aware estimation, where the design of GME matrix is a key to guarantee the overall convexity of the model. The proposed design is applicable to general linear operators involved in the regularizer of the LiGME model, and does not require any eigendecomposition or iterative computation. We also present an application of the LiGME model with the proposed GME matrix to a group sparsity aware least squares estimation problem. Numerical experiments demonstrate the effectiveness of the proposed GME matrix in the LiGME model.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAP1118/_p
부
@ARTICLE{e106-a_8_1025,
author={Yang CHEN, Masao YAMAGISHI, Isao YAMADA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Unified Design of Generalized Moreau Enhancement Matrix for Sparsity Aware LiGME Models},
year={2023},
volume={E106-A},
number={8},
pages={1025-1036},
abstract={In this paper, we propose a unified algebraic design of the generalized Moreau enhancement matrix (GME matrix) for the Linearly involved Generalized-Moreau-Enhanced (LiGME) model. The LiGME model has been established as a framework to construct linearly involved nonconvex regularizers for sparsity (or low-rank) aware estimation, where the design of GME matrix is a key to guarantee the overall convexity of the model. The proposed design is applicable to general linear operators involved in the regularizer of the LiGME model, and does not require any eigendecomposition or iterative computation. We also present an application of the LiGME model with the proposed GME matrix to a group sparsity aware least squares estimation problem. Numerical experiments demonstrate the effectiveness of the proposed GME matrix in the LiGME model.},
keywords={},
doi={10.1587/transfun.2022EAP1118},
ISSN={1745-1337},
month={August},}
부
TY - JOUR
TI - A Unified Design of Generalized Moreau Enhancement Matrix for Sparsity Aware LiGME Models
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1025
EP - 1036
AU - Yang CHEN
AU - Masao YAMAGISHI
AU - Isao YAMADA
PY - 2023
DO - 10.1587/transfun.2022EAP1118
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2023
AB - In this paper, we propose a unified algebraic design of the generalized Moreau enhancement matrix (GME matrix) for the Linearly involved Generalized-Moreau-Enhanced (LiGME) model. The LiGME model has been established as a framework to construct linearly involved nonconvex regularizers for sparsity (or low-rank) aware estimation, where the design of GME matrix is a key to guarantee the overall convexity of the model. The proposed design is applicable to general linear operators involved in the regularizer of the LiGME model, and does not require any eigendecomposition or iterative computation. We also present an application of the LiGME model with the proposed GME matrix to a group sparsity aware least squares estimation problem. Numerical experiments demonstrate the effectiveness of the proposed GME matrix in the LiGME model.
ER -