Structured and Unstructured Outlier Identification for Robust PCA: A Non iterative, Parameter free Algorithm
This addresses a practical problem in data analysis for applications where outlier parameters are unknown, offering a computationally efficient solution, though it is incremental as it builds on existing robust PCA models.
The paper tackles robust PCA without prior knowledge of outlier fraction or subspace dimension, proposing a parameter-free algorithm that identifies both structured and unstructured outliers. It demonstrates competitive performance with state-of-the-art methods on real and synthetic data, with analytical guarantees provided.
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.