We describe and analyze a simple algorithm for principal component analysis, VR-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.
The first analysis for nonconvex variance reduced stochastic gradient is due to REF , who apply it to the specific problem of principal component analysis (PCA).
A Stochastic PCA and SVD Algorithm with an Exponential Convergence Rate
ArXiv
ArXiv
Computer Science Mathematics