Fast, Parameter free Outlier Identification for Robust PCA

TL;DR

This paper introduces a fast, parameter-free method for outlier detection in robust PCA that does not require prior knowledge of outlier fraction or subspace dimension, with proven guarantees and competitive performance.

Contribution

It proposes a novel outlier identification algorithm for robust PCA that is simple, fast, and does not depend on prior parameter knowledge, unlike existing methods.

Findings

Algorithm is computationally simple and fast.

Analytical guarantees are provided for outlier detection.

Performance compares favorably with state-of-the-art methods.

Abstract

Robust PCA, the problem of PCA in the presence of outliers has been extensively investigated in the last few years. Here we focus on Robust PCA in the column sparse outlier model. The existing methods for column sparse outlier model assumes either the knowledge of the dimension of the lower dimensional subspace or the fraction of outliers in the system. However in many applications knowledge of these parameters is not available. Motivated by this we propose a parameter free outlier identification method for robust PCA which a) does not require the knowledge of outlier fraction, b) does not require the knowledge of the dimension of the underlying subspace, c) is computationally simple and fast. Further, analytical guarantees are derived for outlier identification and the performance of the algorithm is compared with the existing state of the art methods.