May 7, 2018

In our recent paper, we present a high-dimensional analysis of three popular algorithms, namely, Oja's method, GROUSE and PETRELS, for subspace estimation from streaming and highly incomplete observations. We show that, with proper time scaling, the time-varying principal angles between the true subspace and its estimates given by the algorithms converge weakly to deterministic processes when the ambient dimension \(n\) tends to infinity. Moreover, the limiting processes can be exactly characterized as the unique solutions of certain ordinary differential equations (ODEs). A finite sample bound is also given, showing that the rate of convergence towards such limits is \(\mathcal{O}(1/\sqrt{n})\).