Efficient Structured Matrix Rank Minimization

Abstract

We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use the full SVD; nor (b) resort to augmented Lagrangian techniques; nor (c) solve linear systems per iteration. Instead, we formulate the problem differently so that it is amenable to a generalized conditional gradient method, which results in a practical improvement with low per iteration computational cost. Numerical results show that our approach significantly outperforms state-of-the-art competitors in terms of running time, while effectively recovering low rank solutions in stochastic system realization and spectral compressed sensing problems.

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Cite this paper

@inproceedings{Yu2014EfficientSM, title={Efficient Structured Matrix Rank Minimization}, author={Adams Wei Yu and Wanli Ma and Yaoliang Yu and Carlos de Juan Carbonell and Suvrit Sra}, booktitle={NIPS}, year={2014} }