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A Stochastic PCA and SVD Algorithm with an Exponential Convergence Rate

2020-03-05 | |  70 |   48 |   0

Abstract

We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converge 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 variancereduced stochastic gradient technique, which was previously analyzed for strongly convex optimization, whereas here we apply it to an inherently non-convex problem, using a very different analysis.

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