On the equivalence between low-rank matrix completion and tensor rank

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On the equivalence between low rank matrix completion and tensor rank

Abstract. The Rank Minimization Problem asks to find a matrix of lowest rank inside a linear variety of the space of n×m matrices. The Low Rank Matrix Completion problem asks to complete a partially filled matrix such that the resulting matrix has smallest possible rank. The Tensor Rank Problem asks to determine the rank of a tensor. We show that these three problems are equivalent: each one of...

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While datasets are frequently represented as matrices, real-word data is imperfect and entries are often missing. In many cases, the data are very sparse and the matrix must be filled in before any subsequent work can be done. This optimization problem, known as matrix completion, can be made well-defined by assuming the matrix to be low rank. The resulting rank-minimization problem is NP-hard,...

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ژورنال

عنوان ژورنال: Linear and Multilinear Algebra

سال: 2017

ISSN: 0308-1087,1563-5139

DOI: 10.1080/03081087.2017.1315044