Nearly Optimal Robust Subspace Tracking

Understand

In this work, we study the robust subspace tracking (RST) problem and obtain one of the first two provable guarantees for it.

• The goal of RST is to track sequentially arriving data vectors that lie in a slowly changing low-dimensional subspace, while being robust to corruption by additive sparse outliers.
• It can also be interpreted as a dynamic (time-varying) extension of robust PCA (RPCA), with the minor difference that RST also requires a short tracking delay.
• We develop a recursive projected compressive sensing algorithm that we call Nearly Optimal RST via ReProCS (ReProCS-NORST) because its tracking delay is nearly optimal.