Online Estimation of Coherent Subspaces with Adaptive Sampling

This work investigates adaptive sampling strategies for online subspace estimation from streaming input vectors where the underlying subspace is coherent, i.e., aligned with some subset of the coordinate axes. We adapt the previously proposed Grassmannian rank-one update subspace estimation (GROUSE) algorithm to incorporate an adaptive sampling strategy that substantially improves over uniform random sampling. Our approach is to sample some proportion of the entries based on the leverage scores of the current subspace estimate. Experiments on synthetic data demonstrate that the adaptive measurement scheme greatly improves the convergence rate of GROUSE over uniform random measurements when the underlying subspace is coherent.