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

2020-03-05 | |  99 |   58 |   0

Abstract

We study the convergence properties of the VRPCA algorithm introduced by (Shamir, 2015) 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 analysis, and what are the convexity and nonconvexity properties of the underlying optimization problem.

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