Online Robust PCA via Stochastic Optimization

Robust PCA methods are typically based on batch optimization and have to load all the samples into memory. This prevents them from efficiently processing big data. In this paper, we develop an Online Robust Principal Component Analysis (OR-PCA) that processes one sample per time instance and hence its memory cost is independent of the data size, significantly enhancing the computation and storage efficiency. The proposed method is based on stochastic optimization of an equivalent reformulation of the batch RPCA method. Indeed, we show that OR-PCA provides a sequence of subspace estimations converging to the optimum of its batch counterpart and hence is provably robust to sparse corruption.