A decentralized approach to robust subspace recovery

This paper considers subspace recovery in the presence of outliers in a decentralized setting. The intrinsic low-dimensional geometry of the data is exploited to substantially reduce the processing and communication overhead given limited sensing and communication resources at the sensing nodes. A small subset of the data is first selected. The data is embedded into a random low-dimensional subspace then forwarded to a central processing unit that runs a low-complexity algorithm to recover the subspace directly from the data sketch. We derive sufficient conditions on the compression and communication rates to successfully recover the subspace with high probability. It is shown that the proposed approach is robust to outliers and its complexity is independent of the dimension of the whole data matrix. The proposed algorithm provably achieves notable speedups in comparison to existing approaches for robust subspace recovery.