Stochastic Gauss-Newton Algorithms for Online PCA

TL;DR

This paper introduces a stochastic Gauss-Newton algorithm for online PCA that improves robustness, includes an adaptive stepsize strategy, and proves convergence without eigengap assumptions.

Contribution

The paper presents a novel stochastic Gauss-Newton algorithm for online PCA, with an adaptive stepsize and proven convergence properties.

Findings

SGN shows improved robustness over existing methods.

AdaSGN performs comparably to manually-tuned algorithms.

Convergence is established without eigengap assumptions.

Abstract

In this paper, we propose a stochastic Gauss-Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is formulated by using the symmetric low-rank product (SLRP) model for dominant eigenspace calculation. Compared with existing OPCA solvers, SGN is of improved robustness with respect to the varying input data and algorithm parameters. In addition, turning to an evaluation of data stream based on approximated objective functions, we develop a new adaptive stepsize strategy for SGN (AdaSGN) which requires no priori knowledge of the input data, and numerically illustrate its comparable performance with SGN adopting the manaully-tuned diminishing stepsize. Without assuming the eigengap to be positive, we also establish the global and optimal convergence rate of SGN with the specified stepsize using the diffusion approximation theory.