Reweighted l1 Algorithm for Robust Principal Component Analysis

In this work, we consider the Robust Principal Components Analysis, a popular method of dimensionality reduction. The corresponding optimization involves the minimization of l(0)-norm which is known to be NP-hard. To deal with this problem, we replace the l(0)-norm by a non-convex approximation, namely capped l(1)DD-norm. The resulting optimization problem is non-convex for which we develop a reweighted l(1) based algorithm. Numerical experiments on several synthetic datasets illustrate the efficiency of our algorithm and its superiority comparing to several state-of-the-art algorithms.