Efficient Structured Matrix Rank Minimization

Part of Advances in Neural Information Processing Systems 27 (NIPS 2014)

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Authors

Adams Wei Yu, Wanli Ma, Yaoliang Yu, Jaime Carbonell, Suvrit Sra

Abstract

<p>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.</p>