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 data set 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 emphasizes advantages and disadvantages of proposed approaches and unsolved problems in the area.
Bibliographical noteFunding Information:
Manuscript received March 1, 2018; revised June 5, 2018; accepted June 29, 2018. Date of current version August 2, 2018. This work was supported by the National Science Foundation (NSF) under Grant DMS-14-18386 and by a University of Minnesota Doctoral Dissertation Fellowship. (Corresponding author: Gilad Lerman.) The authors are with the Department of Mathematics, University of Minnesota, Minneapolis, MN 55116 USA (e-mail: email@example.com; firstname.lastname@example.org).
- Big data
- Dimension reduction
- Nonconvex optimization
- Recovery guarantees
- Subspace modeling
- Unsupervised learning