An Acceleration Scheme for Memory Limited, Streaming PCA
This work addresses the challenge of efficient PCA for streaming data in fields like simulations, though it appears incremental as it builds on existing online PCA methods.
The paper tackles the problem of performing PCA in memory-limited, streaming data scenarios by proposing an acceleration scheme that converges to the first k eigenvectors in a single data pass, with empirical results based on the spiked covariance model and applications to time-varying systems like Molecular Dynamics simulations.
In this paper, we propose an acceleration scheme for online memory-limited PCA methods. Our scheme converges to the first $k>1$ eigenvectors in a single data pass. We provide empirical convergence results of our scheme based on the spiked covariance model. Our scheme does not require any predefined parameters such as the eigengap and hence is well facilitated for streaming data scenarios. Furthermore, we apply our scheme to challenging time-varying systems where online PCA methods fail to converge. Specifically, we discuss a family of time-varying systems that are based on Molecular Dynamics simulations where batch PCA converges to the actual analytic solution of such systems.