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".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Neste artigo, propomos um projeto algébrico unificado da matriz de aprimoramento de Moreau generalizada (matriz GME) para o modelo Linearmente envolvido Generalizado-Moreau-Enhanced (LiGME). O modelo LiGME foi estabelecido como uma estrutura para construir regularizadores não convexos envolvidos linearmente para estimativa consciente de esparsidade (ou classificação baixa), onde o design da matriz GME é uma chave para garantir a convexidade geral do modelo. O projeto proposto é aplicável a operadores lineares gerais envolvidos no regularizador do modelo LiGME e não requer qualquer composição própria ou computação iterativa. Apresentamos também uma aplicação do modelo LiGME com a matriz GME proposta para um problema de estimativa de mínimos quadrados com conhecimento de esparsidade de grupo. Experimentos numéricos demonstram a eficácia da matriz GME proposta no modelo LiGME.
Yang CHEN
Tokyo Institute of Technology
Masao YAMAGISHI
Tokyo Institute of Technology
Isao YAMADA
Tokyo Institute of Technology
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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
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@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},}
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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 -