Journal of the
Korean Mathematical Society JKMS

It is computationally expensive to compute principal components from scratch at every update or downdate when new data arrive and existing data are truncated from the data matrix frequently. To overcome this limitations, incremental principal component analysis is considered. Specifically, we present a sliding window based efficient incremental principal component computation from a covariance matrix which comprises of two procedures; simultaneous update and downdate of principal components, followed by the rank-one matrix update. Additionally we track the accurate decomposition error and the adaptive numerical rank. Experiments show that the proposed algorithm enables a faster execution speed and no-meaningful decomposition error differences compared to typical incremental principal component analysis algorithms, thereby maintaining a good approximation for the principal components.

Keywords: Incremental principal components analysis, sliding window

MSC numbers: Primary 15A18, 15A23

Supported by: This work was supported by Hankuk University of Foreign Studies Research Fund and National Research Foundation of Korea (NRF) grant funded by the Korean government (2018R1C1B5085022).