Robust principal component analysis

Robust Principal Component Analysis (RPCA) is a modification of the widely used statistical procedure Principal component analysis (PCA) which works pretty well with respect to grossly corrupted observations. Several number of approaches exist for Robust PCA, including an idealized version of Robust PCA, in which we aim to recover a low-rank matrix L₀ from highly corrupted measurements M = L₀ +S₀.

Applications

RPCA has many real life important applications particularly when the data under study can naturally be modeled as a low-rank plus a sparse contribution. Following examples are inspired by contemporary challenges in computer science, and depending on the applications, either the low-rank component or the sparse component could be the object of interest:

Video Surveillance

Given a sequence of surveillance video frames, it is often required to identify the activities that stand out from the background. If we stack the video frames as columns of a matrix M , then the low-rank component L₀ naturally corresponds to the stationary background and the sparse component S₀ captures the moving objects in the foreground.