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.

中文翻译：

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从排列中恢复矩阵


在数据科学中，已经出现了许多涉及从排列中恢复数据的应用程序。在这里，我们从理论上研究了以秩亏矩阵组织的数据的这个问题。具体来说，我们为已对其条目进行任意排列的有界​​秩矩阵提供独特的恢复保证。我们使用交换代数和代数几何的方法和结果，为此我们为普通观众做了准备。