Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion
Machine Learning
2013-04-02 v2 Algebraic Geometry
Combinatorics
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.
Keywords
Cite
@article{arxiv.1302.5337,
title = {Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion},
author = {Franz J. Király and Louis Theran},
journal= {arXiv preprint arXiv:1302.5337},
year = {2013}
}
Comments
14 pages with appendix, 2 figures, v2 adds larger experiments and smoother exposition