Journal
STATISTICS AND COMPUTING
Volume 26, Issue 1-2, Pages 409-421Publisher
SPRINGER
DOI: 10.1007/s11222-014-9485-x
Keywords
FACE; fPCA; Penalized splines; Sandwich smoother; Smoothing; Singular value decomposition
Funding
- National Institute of Biomedical Imaging And Bioengineering [R01EB012547]
- National Institute of Neurological Disorders and Stroke [R01NS060910]
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We propose two fast covariance smoothing methods and associated software that scale up linearly with the number of observations per function. Most available methods and software cannot smooth covariance matrices of dimension J > 500; a recently introduced sandwich smoother is an exception but is not adapted to smooth covariance matrices of large dimensions, such as J = 10,000. We introduce two new methods that circumvent those problems: (1) a fast implementation of the sandwich smoother for covariance smoothing; and (2) a two-step procedure that first obtains the singular value decomposition of the data matrix and then smoothes the eigenvectors. These new approaches are at least an order of magnitude faster in high dimensions and drastically reduce computer memory requirements. The new approaches provide instantaneous (a few seconds) smoothing for matrices of dimension J = 10,000 and very fast (< 10 min) smoothing for J = 100,000. R functions, simulations, and data analysis provide ready to use, reproducible, and scalable tools for practical data analysis of noisy high-dimensional functional data.
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