An Iterative Method for Structured Matrix Completion
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The task of filling-in or predicting missing entries of a matrix, from a subset of known entries, is known as matrix completion. In today's data-driven world, data completion is essential whether it is the main goal or a pre-processing step. In recent work, a modification to the standard nuclear norm minimization for matrix completion has been made to take into account structural differences between observed and unobserved entries. One example of such structural difference is when the probability that an entry is observed or not depends mainly on the value of the entry. We propose adjusting an Iteratively Reweighted Least Squares (IRLS) algorithm for low-rank matrix completion to take into account sparsity-based structure in the missing entries. We also present an iterative gradient-projection-based implementation of the algorithm, and present numerical experiments showing that the proposed method often outperforms the IRLS algorithm in structured settings.
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