仿等级最小化问题的随机方差降低梯度

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-06-04 DOI:10.1137/23m1555387

Ningning Han, Juan Nie, Jian Lu, Michael K. Ng

{"title":"仿等级最小化问题的随机方差降低梯度","authors":"Ningning Han, Juan Nie, Jian Lu, Michael K. Ng","doi":"10.1137/23m1555387","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1118-1144, June 2024. <br/> Abstract.In this paper, we develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consisting of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic gradient descent strategy enjoys a more favorable complexity than that using full gradients. It also reduces the variance of the stochastic gradient at each iteration and accelerates the rate of convergence. We prove that the proposed algorithm converges linearly in expectation to the solution under a restricted isometry condition. Numerical experimental results demonstrate that the proposed algorithm has a clear advantageous balance of efficiency, adaptivity, and accuracy compared with other state-of-the-art algorithms.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"32 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stochastic Variance Reduced Gradient for Affine Rank Minimization Problem\",\"authors\":\"Ningning Han, Juan Nie, Jian Lu, Michael K. Ng\",\"doi\":\"10.1137/23m1555387\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1118-1144, June 2024. <br/> Abstract.In this paper, we develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consisting of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic gradient descent strategy enjoys a more favorable complexity than that using full gradients. It also reduces the variance of the stochastic gradient at each iteration and accelerates the rate of convergence. We prove that the proposed algorithm converges linearly in expectation to the solution under a restricted isometry condition. Numerical experimental results demonstrate that the proposed algorithm has a clear advantageous balance of efficiency, adaptivity, and accuracy compared with other state-of-the-art algorithms.\",\"PeriodicalId\":49528,\"journal\":{\"name\":\"SIAM Journal on Imaging Sciences\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Imaging Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1555387\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Imaging Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1555387","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 影像科学期刊》第 17 卷第 2 期第 1118-1144 页，2024 年 6 月。摘要.在本文中，我们开发了一种高效的随机方差降低梯度下降算法来解决仿射秩最小化问题，该问题包括从线性测量中找到秩最小的矩阵。作为一种随机梯度下降策略，所提出的算法比使用完全梯度的算法具有更高的复杂度。它还降低了每次迭代的随机梯度方差，加快了收敛速度。我们证明了所提出的算法在受限等距条件下线性收敛于期望解。数值实验结果表明，与其他最先进的算法相比，所提出的算法在效率、适应性和准确性之间具有明显的平衡优势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Stochastic Variance Reduced Gradient for Affine Rank Minimization Problem

SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1118-1144, June 2024.
Abstract.In this paper, we develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consisting of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic gradient descent strategy enjoys a more favorable complexity than that using full gradients. It also reduces the variance of the stochastic gradient at each iteration and accelerates the rate of convergence. We prove that the proposed algorithm converges linearly in expectation to the solution under a restricted isometry condition. Numerical experimental results demonstrate that the proposed algorithm has a clear advantageous balance of efficiency, adaptivity, and accuracy compared with other state-of-the-art algorithms.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Imaging Sciences COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

3.80

自引率

4.80%

发文量

审稿时长

>12 weeks

期刊介绍： SIAM Journal on Imaging Sciences (SIIMS) covers all areas of imaging sciences, broadly interpreted. It includes image formation, image processing, image analysis, image interpretation and understanding, imaging-related machine learning, and inverse problems in imaging; leading to applications to diverse areas in science, medicine, engineering, and other fields. The journal’s scope is meant to be broad enough to include areas now organized under the terms image processing, image analysis, computer graphics, computer vision, visual machine learning, and visualization. Formal approaches, at the level of mathematics and/or computations, as well as state-of-the-art practical results, are expected from manuscripts published in SIIMS. SIIMS is mathematically and computationally based, and offers a unique forum to highlight the commonality of methodology, models, and algorithms among diverse application areas of imaging sciences. SIIMS provides a broad authoritative source for fundamental results in imaging sciences, with a unique combination of mathematics and applications. SIIMS covers a broad range of areas, including but not limited to image formation, image processing, image analysis, computer graphics, computer vision, visualization, image understanding, pattern analysis, machine intelligence, remote sensing, geoscience, signal processing, medical and biomedical imaging, and seismic imaging. The fundamental mathematical theories addressing imaging problems covered by SIIMS include, but are not limited to, harmonic analysis, partial differential equations, differential geometry, numerical analysis, information theory, learning, optimization, statistics, and probability. Research papers that innovate both in the fundamentals and in the applications are especially welcome. SIIMS focuses on conceptually new ideas, methods, and fundamentals as applied to all aspects of imaging sciences.