ABSTRACT
RPCA via decomposition in low-rank and sparse matrices proposed by Candes et al. [20] in 2009 is currently the most investigated RPCA method. In this chapter, we review this method and all these modifications in terms of decomposition, solvers, incremental algorithms, and real-time implementations. These different RPCA methods via decomposition in low-rank and sparse matrices are fundamental in several applications [21]. Indeed, as this decomposition is nonparametric and does not make many assumptions, it is widely applicable to a large scale of problems that include the following:
• Latent variable model selection: Chandrasekaran et al. [24] proposed to discover the number of latent components, and to learn a statistical model over the entire collection of variables by only observing samples of a subset of a collection of random variables. The geometric properties of the decompostion of low-rank plus sparse matrices play an important role in this approach [24] [108].
