An Efficient Randomized Low-Rank Matrix Factorization with Application to Robust PCA

Low-rank matrix factorization algorithms using the randomized sampling paradigm have recently gained momentum, owing to their computational efficiency, high accuracy, robustness, and efficient parallelization. This paper presents a randomized factorization algorithm tailored for low-rank matrices, called Randomized Partial UTV (RaP-UTV) factorization. RaP-Utvis efficient in arithmetic operations, and can harness the parallel structure of advanced computational platforms. The effectiveness of RaP-Utvis demonstrated through synthetic and real-world data. Applications treated in this work include image reconstruction and robust principal component analysis. The results of RaP-UTV are compared with those of multiple algorithms from the literature.