A Stochastic PCA and SVD Algorithm with an Exponential Convergence Rate

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 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 an inherently non-convex problem, using a very different analysis.

Fixed a minor bug in the proof of lemma 1 (which does not affect the result)

References in corpus (3)

• The Noisy Power Method: A Meta Algorithm with Applications
• Global Convergence of Stochastic Gradient Descent for Some Non-convex Matrix Problems
• Stochastic Optimization of PCA with Capped MSG

Cited by in corpus (6)

• Stochastic Variance Reduction for Nonconvex Optimization
• Fast Incremental Method for Nonconvex Optimization
• Correlated-PCA: Principal Components' Analysis when Data and Noise are Correlated
• Noisy Accelerated Power Method for Eigenproblems with Applications
• Variance-Reduced Proximal Stochastic Gradient Descent for Non-convex Composite optimization
• Adaptive PCA for Time-Varying Data