Structured and Unstructured Outlier Identification for Robust PCA: A Non iterative, Parameter free Algorithm

TL;DR

This paper introduces a fast, parameter-free algorithm for robust PCA that effectively identifies outliers without prior knowledge of subspace dimension or outlier fraction, handling both structured and unstructured outliers.

Contribution

A novel outlier detection method for robust PCA that is parameter-free, computationally simple, and applicable to various outlier structures, with analytical guarantees.

Findings

Performs well on real and synthetic data

Outperforms existing methods in outlier detection accuracy

Handles both structured and unstructured outliers

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 outlier model where each column of the data matrix is either an inlier or an outlier. Most of the existing methods for this 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 d) can handle structured and unstructured outliers. Further, analytical guarantees are derived for outlier identification and the performance of the algorithm is compared with the existing state of the art methods in both real and synthetic data for various outlier structures.