从排列中恢复矩阵

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-07-14 DOI:10.1016/j.acha.2024.101688

Manolis C. Tsakiris

{"title":"从排列中恢复矩阵","authors":"Manolis C. Tsakiris","doi":"10.1016/j.acha.2024.101688","DOIUrl":null,"url":null,"abstract":"<div><p>In data science, a number of applications have been emerging involving data recovery from permutations. Here, we study this problem theoretically for data organized in a rank-deficient matrix. Specifically, we give unique recovery guarantees for matrices of bounded rank that have undergone arbitrary permutations of their entries. We use methods and results of commutative algebra and algebraic geometry, for which we include a preparation for a general audience.</p></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"73 ","pages":"Article 101688"},"PeriodicalIF":2.6000,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Matrix recovery from permutations\",\"authors\":\"Manolis C. Tsakiris\",\"doi\":\"10.1016/j.acha.2024.101688\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In data science, a number of applications have been emerging involving data recovery from permutations. Here, we study this problem theoretically for data organized in a rank-deficient matrix. Specifically, we give unique recovery guarantees for matrices of bounded rank that have undergone arbitrary permutations of their entries. We use methods and results of commutative algebra and algebraic geometry, for which we include a preparation for a general audience.</p></div>\",\"PeriodicalId\":55504,\"journal\":{\"name\":\"Applied and Computational Harmonic Analysis\",\"volume\":\"73 \",\"pages\":\"Article 101688\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-07-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied and Computational Harmonic Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1063520324000654\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied and Computational Harmonic Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1063520324000654","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

在数据科学中，出现了许多涉及从排列中恢复数据的应用。在这里，我们从理论上研究了秩不足矩阵中的数据恢复问题。具体来说，我们给出了对其条目经过任意排列的有界秩矩阵的唯一恢复保证。我们使用了交换代数和代数几何的方法和结果，其中包括为普通读者准备的内容。

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

Matrix recovery from permutations

In data science, a number of applications have been emerging involving data recovery from permutations. Here, we study this problem theoretically for data organized in a rank-deficient matrix. Specifically, we give unique recovery guarantees for matrices of bounded rank that have undergone arbitrary permutations of their entries. We use methods and results of commutative algebra and algebraic geometry, for which we include a preparation for a general audience.

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

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.