Reviews: Diffusion Approximations for Online Principal Component Estimation and Global Convergence

They show it can be approximated using a stochastic process and provide global convergence guarantees which match the optimal . Although the related work section is very dense, it is well organized and serves as a good starting point for the non-expert reader. As a non expert in this area I find it quite hard to judge the merits of this paper in detail. Having said that it seems that providing the first global convergence guarantees for Oja's rule ought to be of interest. The analysis seems to thoroughly explain the different phases in the optimization procedure which perhaps could be useful as a diagnostic tool.