Welcome!
| Credits | People |
This website introduces new tools for recovering low-rank matrices from incomplete or corrupted observations.
A common modeling assumption in many engineering applications is that the underlying data lies (approximately) on a low-dimensional linear subspace. This property has been widely exploited by classical Principal Component Analysis (PCA) to achieve dimensionality reduction. However, real-life data is often corrupted with large errors or can even be incomplete. Although classical PCA is effective against the presence of small Gaussian noise in the data, it is highly sensitive to even sparse errors of very high magnitude.
We propose powerful tools that exactly and efficiently correct large errors in such structured data. The basic idea is to formulate the problem as a matrix rank minimization problem and solve it efficiently by nuclear-norm minimization. Our algorithms achieve state-of-the-art performance in low-rank matrix recovery with theoretical guarantees. Please browse the links to the left for more information. The introduction section provides a brief overview of the low-rank matrix recovery problem and introduces state-of-the-art algorithms to solve. Please refer to our papers in the references section for complete technical details, and to the sample code section for MATLAB packages. The applications section showcases engineering problems where our techniques have been used to achieve state-of-the-art performance.
Credits
This website is maintained by the research group of Prof. Yi Ma at the University of Illinois at Urbana-Champaign. This work was partially supported by the grants: NSF IIS 08-49292, NSF ECCS 07-01676, ONR N00014-09-1-0230, ONR N00014-09-1-0230, NSF CCF 09-64215, NSF ECCS 07-01676, and NSF IIS 11-16012. Any opinions, findings, and conclusions or recommendations expressed in our publications are those of the respective authors and do not necessarily reflect the views of the National Science Foundation or Office of Naval Research.
Please direct your comments and questions to the webmaster - Kerui Min.
People
 Matrix of corrupted observations |
 |
 Underlying low-rank matrix |
+ |  Sparse error matrix
|
A common modeling assumption in many engineering applications is that the underlying data lies (approximately) on a low-dimensional linear subspace. This property has been widely exploited by classical Principal Component Analysis (PCA) to achieve dimensionality reduction. However, real-life data is often corrupted with large errors or can even be incomplete. Although classical PCA is effective against the presence of small Gaussian noise in the data, it is highly sensitive to even sparse errors of very high magnitude.
We propose powerful tools that exactly and efficiently correct large errors in such structured data. The basic idea is to formulate the problem as a matrix rank minimization problem and solve it efficiently by nuclear-norm minimization. Our algorithms achieve state-of-the-art performance in low-rank matrix recovery with theoretical guarantees. Please browse the links to the left for more information. The introduction section provides a brief overview of the low-rank matrix recovery problem and introduces state-of-the-art algorithms to solve. Please refer to our papers in the references section for complete technical details, and to the sample code section for MATLAB packages. The applications section showcases engineering problems where our techniques have been used to achieve state-of-the-art performance.
Credits
This website is maintained by the research group of Prof. Yi Ma at the University of Illinois at Urbana-Champaign. This work was partially supported by the grants: NSF IIS 08-49292, NSF ECCS 07-01676, ONR N00014-09-1-0230, ONR N00014-09-1-0230, NSF CCF 09-64215, NSF ECCS 07-01676, and NSF IIS 11-16012. Any opinions, findings, and conclusions or recommendations expressed in our publications are those of the respective authors and do not necessarily reflect the views of the National Science Foundation or Office of Naval Research.
Please direct your comments and questions to the webmaster - Kerui Min.
People
- Prof. John Wright (Assistant Professor, Columbia University)
- Arvind Ganesh (PhD student, ECE, UIUC)
- Zihan Zhou (PhD student, ECE, UIUC)
- Kerui Min (PhD student, ECE, UIUC)
- Dr. Shankar Rao (Research Staff Member, HRL Laboratories)
- Dr. Zhouchen Lin (Lead Researcher, Microsoft Research Asia)
- Yigang Peng (PhD student, Tsinghua University)
- Minming Chen (Graduate student, Chinese Academy of Sciences)
- Leqin Wu (Graduate student, Chinese Academy of Sciences)
- Prof. Yi Ma (Associate Professor, ECE, UIUC)
- Prof. Emmanuel Candès (Professor, Stanford University)
- Xiaodong Li (PhD student, Stanford University)