Robust Principal Component Analysis

Robust Principal Component Analysis (RPCA) aims to decompose a data matrix into a low-rank component representing the underlying structure and a sparse component representing outliers or noise, overcoming the limitations of standard PCA in the presence of corrupted data. Current research focuses on developing computationally efficient algorithms, including those based on iterative methods like alternating projections and gradient descent, deep unfolding networks, and novel matrix/tensor decompositions (e.g., CUR, Tucker, Tensor Train), often incorporating regularization techniques to enhance robustness and scalability. These advancements are significant for various applications, improving the accuracy and efficiency of data analysis in fields ranging from image processing and video analysis to anomaly detection and time series forecasting.