Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion

Franz J. Király; Louis Theran

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arXiv · 1302.5337

Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion

Franz J. Király·Louis Theran

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Abstract

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless case our algorithm is exact. For rank-one matrices, the new algorithm is fast, admits a highly-parallel implementation, and produces an error minimizing estimate that is qualitatively close to our theoretical and the state-of-the-are Nuclear Norm and OptSpace methods.

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BibTeX RIS

Franz J. Király, Louis Theran. 2013-02-21. Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion. https://arxiv.org/abs/1302.5337

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