Double-noise-dual-problem approach to the augmented Lagrange multiplier method for robust principal component analysis

Abstract

Robust principal component analysis (RPCA) is one of the most useful tools to recover a low-rank data component from the superposition of a sparse component. The augmented Lagrange multiplier (ALM) method enjoys the highest accuracy among all the approaches to the RPCA. However, it still suffers from two problems, namely, a brutal force initialization phase resulting in low convergence speed and ignorance of other types of noise resulting in low accuracy. To this end, this paper proposes a double-noise, dual-problem approach to the augmented Lagrange multiplier method, referred to as DNDP-ALM, for robust principal component analysis. Firstly, the original ALM method considers sparse noise only, ignoring Gaussian noise, which generally exists in real-world data. In our proposed DNDP-ALM, the data consist of low-rank component, sparse component and Gaussian noise component, with RPCA problem converted to convex optimization. Secondly, the original ALM uses a rough initialization of multipliers, leading to more work of iterative calculation and lower calculation accuracy. In our proposed DNDP-ALM, the initialization is carried out by solving a dual problem to obtain the optimal multiplier. The experimental results show that the proposed approach super-performs in solving robust principal component analysis problems in terms of speed and accuracy, compared to the state-of-the-art techniques.