{"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}
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.
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.
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