一维张量网络恢复

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-07-01 DOI:10.1137/23m159888x

Ziang Chen, Jianfeng Lu, Anru Zhang

{"title":"一维张量网络恢复","authors":"Ziang Chen, Jianfeng Lu, Anru Zhang","doi":"10.1137/23m159888x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1217-1244, September 2024. <br/> Abstract. We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is [math] for [math]th-order tensors. We prove that our algorithms can almost surely recover the correct graph or permutation when tensor entries can be observed without noise. We further establish the robustness of our algorithms against observational noise. The theoretical results are validated by numerical experiments.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"7 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"One-Dimensional Tensor Network Recovery\",\"authors\":\"Ziang Chen, Jianfeng Lu, Anru Zhang\",\"doi\":\"10.1137/23m159888x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1217-1244, September 2024. <br/> Abstract. We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is [math] for [math]th-order tensors. We prove that our algorithms can almost surely recover the correct graph or permutation when tensor entries can be observed without noise. We further establish the robustness of our algorithms against observational noise. The theoretical results are validated by numerical experiments.\",\"PeriodicalId\":49538,\"journal\":{\"name\":\"SIAM Journal on Matrix Analysis and Applications\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Matrix Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m159888x\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Matrix Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m159888x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 矩阵分析与应用期刊》，第 45 卷第 3 期，第 1217-1244 页，2024 年 9 月。摘要我们研究了张量环或张量列车格式中张量的底层图或排列的恢复。我们提出的算法比较了向下采样后的矩阵化等级，对于[math]阶张量，其复杂度为[math]。我们证明，当张量条目可以无噪声观测时，我们的算法几乎肯定能恢复正确的图或排列。我们进一步确定了我们的算法对观测噪声的鲁棒性。数值实验验证了理论结果。

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

One-Dimensional Tensor Network Recovery

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1217-1244, September 2024.
Abstract. We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is [math] for [math]th-order tensors. We prove that our algorithms can almost surely recover the correct graph or permutation when tensor entries can be observed without noise. We further establish the robustness of our algorithms against observational noise. The theoretical results are validated by numerical experiments.

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 Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.