Distributed Robust Subspace Recovery
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We study Robust Subspace Recovery (RSR) in distributed settings. We consider a huge data set in an ad hoc network without a central processor, where each node has access only to one chunk of the data set. We assume that part of the whole data set lies around a low-dimensional subspace and the other part is composed of outliers that lie away from that subspace. The goal is to recover the underlying subspace for the whole data set, without transferring the data itself between the nodes. We apply the Consensus Based Gradient method for the Geometric Median Subspace algorithm for RSR. We propose an iterative solution for the local dual minimization problem and establish its r-linear convergence. We show that this mathematical framework also extends to two simpler problems: Principal Component Analysis and the geometric median. We also explain how to distributedly implement the Reaper and Fast Median Subspace algorithms for RSR. We demonstrate the competitive performance of our algorithms for both synthetic and real data.
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