Structured and Unstructured Outlier Identification for Robust PCA: A Fast Parameter Free Algorithm

摘要

Robust principal component analysis (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 assume 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 that first, does not require the knowledge of outlier fraction; second, does not require the knowledge of the dimension of the underlying subspace; third, is computationally simple and fast; and fourth, can handle both structured and unstructured outliers. Furthermore, 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.