Fast, Parameter free Outlier Identification for Robust PCA
This work addresses the challenge of robust PCA for applications where outlier parameters are unknown, offering a practical solution but is incremental as it builds on existing column sparse outlier models.
The paper tackles the problem of robust PCA in the presence of column sparse outliers by proposing a parameter-free outlier identification method that eliminates the need for prior knowledge of outlier fraction or subspace dimension, achieving computational simplicity and speed with analytical guarantees and competitive performance compared to state-of-the-art methods.
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.