An Overview of Robust Subspace Recovery

Gilad Lerman and Tyler Maunu

An Overview of Robust Subspace Recovery (2018)


Abstract: This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this problem is easy to state, it has been difficult to develop optimal algorithms due to its underlying nonconvexity. This work will emphasize advantages and disadvantages of proposed approaches and unsolved problems in the area.


This work was supported by NSF grant DMS-14-18386 and a University of Minnesota Doctoral Dissertation Fellowship. The authors would also like to thank all who contributed code used in this survey, and in particular, Ery Arias-Castro, Teng Zhang, Xingguo Li, Jiashi Feng, John Goes, Chong You, and Yeshwanth Cherapanamjeri.