Online compressed robust PCA

In this work, we consider the problem of robust principal component analysis (RPCA) for streaming noisy data that has been highly compressed. This problem is prominent when one deals with high-dimensional and large-scale data and data compression is necessary. To solve this problem, we propose an online compressed RPCA algorithm to efficiently recover the low-rank components of raw data. Though data compression incurs severe information loss, we provide deep analysis on the proposed algorithm and prove that the low-rank component can be asymptotically recovered under mild conditions. Compared with other recent works on compressed RPCA, our algorithm reduces the memory cost significantly by processing data in an online fashion and reduces the communication cost by accepting sequential compressed data as input.