ROIPCA: An online memory-restricted PCA algorithm based on rank-one updates
This work addresses the need for efficient PCA in modern applications with large or streaming data, though it appears incremental as it builds on existing online PCA methods.
The authors tackled the problem of performing PCA on large or streaming data with memory constraints by proposing ROIPCA and fROIPCA, two online PCA algorithms based on rank-one updates, demonstrating numerical advantages in accuracy and runtime over existing state-of-the-art methods.
Principal components analysis (PCA) is a fundamental algorithm in data analysis. Its memory-restricted online versions are useful in many modern applications, where the data are too large to fit in memory, or when data arrive as a stream of items. In this paper, we propose ROIPCA and fROIPCA, two online PCA algorithms that are based on rank-one updates. While ROIPCA is typically more accurate, fROIPCA is faster and has comparable accuracy. We show the relation between fROIPCA and an existing popular gradient algorithm for online PCA, and in particular, prove that fROIPCA is in fact a gradient algorithm with an optimal learning rate. We demonstrate numerically the advantages of our algorithms over existing state-of-the-art algorithms in terms of accuracy and runtime.