Functional principal component analysis information
Functional principal component analysis (FPCA) is a statistical method for investigating the dominant modes of variation of functional data. Using this method, a random function is represented in the eigenbasis, which is an orthonormal basis of the Hilbert space L2 that consists of the eigenfunctions of the autocovariance operator. FPCA represents functional data in the most parsimonious way, in the sense that when using a fixed number of basis functions, the eigenfunction basis explains more variation than any other basis expansion. FPCA can be applied for representing random functions,[1] or in functional regression[2] and classification.
^Jones, M. C.; Rice, J. A. (1992). "Displaying the Important Features of Large Collections of Similar Curves". The American Statistician. 46 (2): 140. doi:10.1080/00031305.1992.10475870.
^Yao, F.; Müller, H. G.; Wang, J. L. (2005). "Functional linear regression analysis for longitudinal data". The Annals of Statistics. 33 (6): 2873. arXiv:math/0603132. doi:10.1214/009053605000000660.
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