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Published 2011 | Published
Journal Article Open

Two proposals for robust PCA using semidefinite programming


The performance of principal component analysis suffers badly in the presence of outliers. This paper proposes two novel approaches for robust principal component analysis based on semidefinite programming. The first method, maximum mean absolute deviation rounding, seeks directions of large spread in the data while damping the effect of outliers. The second method produces a low-leverage decomposition of the data that attempts to form a low-rank model for the data by separating out corrupted observations. This paper also presents efficient computational methods for solving these semidefinite programs. Numerical experiments confirm the value of these new techniques.

Additional Information

© 2011 Institute of Mathematical Statistics. Received December 2010. The authors would like to thank the anonymous referees for their thoughtful suggestions, as well as Alex Gittens, Richard Chen, and Stephen Becker for valuable discussions regarding this work. This work has been supported in part by ONR awards N00014-08-1-0883 and N00014-11-1-0025, AFOSR award FA9550-09-1-0643, and a Sloan Fellowship. This research was performed in part while the authors were in residence at the Institute for Pure and Applied Mathematics at the University of California, Los Angeles.

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August 22, 2023
August 22, 2023