fpca_ssvd: Smoothed FPCA via iterative penalized rank one SVDs.

In tidyfun/refundr: Tidier regression with functional data

Smoothed FPCA via iterative penalized rank one SVDs.

Description

Implements the algorithm of Huang, Shen, Buja (2008) for finding smooth right singular vectors of a matrix X containing (contaminated) evaluations of functional random variables on a regular, equidistant grid. If the number of smooth SVs to extract is not specified, the function hazards a guess for the appropriate number based on the asymptotically optimal truncation threshold under the assumption of a low rank matrix contaminated with i.i.d. Gaussian noise with unknown variance derived in Donoho, Gavish (2013). Please note that Donoho, Gavish (2013) should be regarded as experimental for functional PCA, and will typically not work well if you have more observations than grid points.

Usage

fpca_ssvd(
  Y = NULL,
  argvals = NULL,
  npc = NA,
  center = TRUE,
  maxiter = 15,
  tol = 1e-04,
  diffpen = 3,
  gridsearch = TRUE,
  alphagrid = 1.5^(-20:40),
  lower.alpha = 1e-05,
  upper.alpha = 1e+07,
  integration = "trapezoidal"
)

Arguments

Y	data matrix (rows: observations; columns: grid of eval. points)
argvals	the argument values of the function evaluations in Y, defaults to a equidistant grid from 0 to 1. See Details.
npc	how many smooth SVs to try to extract, if NA (the default) the hard thresholding rule of Donoho, Gavish (2013) is used (see Details, References).
center	center Y so that its column-means are 0? Defaults to TRUE
maxiter	how many iterations of the power algorithm to perform at most (defaults to 15)
tol	convergence tolerance for power algorithm (defaults to 1e-4)
diffpen	difference penalty order controlling the desired smoothness of the right singular vectors, defaults to 3 (i.e., deviations from local quadratic polynomials).
gridsearch	use stats::optimize() or a grid search to find GCV-optimal smoothing parameters? defaults to TRUE.
alphagrid	grid of smoothing parameter values for grid search
lower.alpha	lower limit for for smoothing parameter if !gridsearch
upper.alpha	upper limit for smoothing parameter if !gridsearch
integration	ignored, see Details.

Author(s)

Fabian Scheipl

References

Huang, J. Z., Shen, H., and Buja, A. (2008). Functional principal components analysis via penalized rank one approximation. Electronic Journal of Statistics, 2, 678-695

Donoho, D.L., and Gavish, M. (2013). The Optimal Hard Threshold for Singular Values is 4/sqrt(3). eprint arXiv:1305.5870. Available from http://arxiv.org/abs/1305.5870.

tidyfun/refundr documentation built on March 26, 2022, 4:09 p.m.