ROIPCA: an online memory-restricted PCA algorithm based on rank-one updates

Roy Mitz*, Yoel Shkolnisky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article numberiaad025
JournalInformation and Inference
Issue number4
StatePublished - 1 Dec 2023


FundersFunder number
Horizon 2020 Framework Programme
European Research Council
Horizon 2020723991 - CRYOMATH


    • PCA
    • gradient descent
    • memory-restricted PCA
    • online PCA
    • rank-one update
    • streaming PCA


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