[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j190095

AN EFFICIENT ALGORITHM FOR SLIDING WINDOW BASED INCREMENTAL PRINCIPAL COMPONENTS ANALYSIS

Lee, Geunseop (Division of Global Business and Technology Hankuk University of Foreign Studies)

Publication Information

Journal of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 401-414 More about this Journal

Abstract

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;

Citations & Related Records

Reference

1	J. L. Barlow, A. Smoktunowicz, and H. Erbay, Improved Gram-Schmidt type downdating methods, BIT 45 (2005), no. 2, 259-285. https://doi.org/10.1007/s10543-005-0015-2 DOI
2	M. Brand, Fast low-rank modifications of the thin singular value decomposition, Linear Algebra Appl. 415 (2006), no. 1, 20-30. https://doi.org/10.1016/j.laa.2005.07.021 DOI
3	J. R. Bunch and C. P. Nielsen, Updating the singular value decomposition, Numer. Math. 31 (1978/79), no. 2, 111-129. https://doi.org/10.1007/BF01397471 DOI
4	Y. Li, L. Xu, J. Morphett, and R. Jacobs, An integreted algorithm of incremental and robust PCA, Proc. Int. Conf. on Image Processing (2003), 245-248.
5	H. Abdi and L. J. Williams, Principal component analysis, Wiley Interdiscip. Rev. Comput. Stat. 2-4 (2010), pp. 433-459.
6	R. Badeau, G. Richard, and B. David, Sliding window adaptive SVD algorithms, IEEE Trans. Signal Process. 52 (2004), no. 1, 1-10. https://doi.org/10.1109/TSP.2003.820069 DOI
7	C. Pehlevan, T. Hu, and D. B. Chklovskii, A Hebbian/anti-Hebbian neural network for linear subspace learning: a derivation from multidimensional scaling of streaming data, Neural Comput. 27 (2015), no. 7, 1461-1495. https://doi.org/10.1162/neco_a_00745 DOI
8	J. Weng, Y. Zhang, and W. S. Hwang, Candid covariance-free incremental principal component analysis, IEEE Trans. Pattern Anal. Mach. Intell, 25-8 (2003), pp. 1034-1040. DOI
9	H. Zhao, P. C. Yuen, and J. T. Kwok, A novel incremental principal component analysis and its application for face recognition, IEEE Trans. on Sys. Man, and Cybernetics, 36-4 (2006), pp. 873-886. DOI