Fast and Provable Robust PCA VIA Normalized Coherence Pursuit

Abstract

The idea of Innovation Search, initially proposed for data clustering, was recently used for outlier detection where the directions of innovation were utilized to measure the innovation of the data points. We study the Innovation Values computed by the Innovation Search algorithm under a quadratic cost function and it is proved that Innovation Values with the new cost function are equivalent to Leverage Scores. This interesting connection is utilized to establish several theoretical guarantees for a Leverage Score based robust PCA method and to design a new robust PCA method. Numerical and theoretical studies indicate that while the presented approach is fast and closed-form, it outperforms most existing algorithms.