A Stochastic PCA Algorithm with an Exponential Convergence Rate

We describe and analyze a simple algorithm for principal component analysis, SVR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In contrast, existing algorithms suffer either from slow convergence, or computationally intensive iterations whose runtime scales with the data size. The algorithm builds on a recent variance-reduced stochastic gradient technique, which was previously analyzed for strongly convex optimization, whereas here we apply it to the non-convex PCA problem, using a very different analysis. Principal Component Analysis (PCA) is one of the most common tools for unsupervised data analysis and preprocessing. In its simplest possible form1, we are given a dataset of n instances x1, . . . ,xn in R, and are interested in finding a unit vector v which minimizes min w:‖w‖=1 − 1 n n ∑