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A rank minimization heuristic with application to minimum order system approximation
Abstract
We describe a generalization of the trace heuristic that applies to general nonsymmetric, even non-square, matrices, and reduces to the trace heuristic when the matrix is positive semidefinite. The heuristic is to replace the (nonconvex) rank objective with the sum of the singular values of the matrix, which is the dual of the spectral norm. We show that this problem can be reduced to a semidefinite program, hence efficiently solved. To motivate the heuristic, we, show that the dual spectral norm is the convex envelope of the rank on the set of matrices with norm less than one. We demonstrate the method on the problem of minimum-order system approximation.
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Cited by
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Gu, S., Zhang, L., Zuo, W., & Feng, X. (2014) · 2014 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2014.366 · Cited by 2,316
Fast maximum margin matrix factorization for collaborative prediction
Rennie, J. D. M., & Srebro, N. (2005) · Proceedings of the 22nd international conference on Machine learning - ICML '05 · doi:10.1145/1102351.1102441 · Cited by 939
Kernel methods in system identification, machine learning and function estimation: A survey
Pillonetto, G., Dinuzzo, F., Chen, T., De Nicolao, G., & Ljung, L. (2014) · Automatica · doi:10.1016/j.automatica.2014.01.001 · Cited by 741
A Survey on Metric Learning for Feature Vectors and Structured Data
Bellet, A., Habrard, A., & Sebban, M. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1306.6709 · Cited by 494
Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
Liu, Z., & Vandenberghe, L. (2010) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/090755436 · Cited by 490
Metadata
- Authors
- Fazel, M., Hindi, H., & Boyd, S. P.
- Venue
- Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148)
- Publisher
- IEEE
- Published
- 2001
- Pages
- 4734-4739 vol.6
- ISSN
- 0743-1619 (ISSN-L)
- OpenAlex
- W1966096622
- Cited by
- 956
- References
- 0
- FWCI
- 21.27
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Fazel, M., Hindi, H., & Boyd, S. P. (2001). A rank minimization heuristic with application to minimum order system approximation. Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148). https://doi.org/10.1109/acc.2001.945730
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