Exponentially convergent stochastic k-PCA without variance reduction

We show, both theoretically and empirically, that the algorithm naturally adapts to data low-rankness and converges exponentially fast to the ground-truth principal subspace. Notably, our result suggests that despite various recent efforts to accelerate the convergence of stochastic-gradient based methods by adding a O(n)-time variance reduction step, for the k- PCA problem, a truly online SGD variant suffices to achieve exponential convergence on intrinsically low-rank data.