Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity

07/31/2015

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by   Ohad Shamir, et al.

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We study the convergence properties of the VR-PCA algorithm introduced by shamir2015stochastic for fast computation of leading singular vectors. We prove several new results, including a formal analysis of a block version of the algorithm, and convergence from random initialization. We also make a few observations of independent interest, such as how pre-initializing with just a single exact power iteration can significantly improve the runtime of stochastic methods, and what are the convexity and non-convexity properties of the underlying optimization problem.