fpca_face: Functional principal component analysis with fast covariance...
In tidyfun/refundr: Tidier regression with functional data

fpca_face

R Documentation

Functional principal component analysis with fast covariance estimation

Description

A fast implementation of the sandwich smoother (Xiao et al., 2013) for covariance matrix smoothing. Pooled generalized cross validation at the data level is used for selecting the smoothing parameter.

Usage

fpca_face(
  data = NULL,
  Y.pred = NULL,
  argvals = NULL,
  pve = 0.99,
  npc = NULL,
  center = TRUE,
  knots = 35,
  p = 3,
  m = 2,
  lambda = NULL,
  alpha = 1,
  search.grid = TRUE,
  search.length = 100,
  method = "L-BFGS-B",
  lower = -20,
  upper = 20,
  control = NULL
)

Arguments

`data`	a `tf` vector containing the functions to decompose using FPCA. Alternatively, a dataframe with arguments arg, value, id. In either case, data must be observed over a regular grid.
`Y.pred`	if desired, a matrix of functions to be approximated using the FPC decomposition.
`argvals`	numeric; function argument.
`pve`	proportion of variance explained: used to choose the number of principal components.
`npc`	how many smooth SVs to try to extract, if `NA` (the default) the hard thresholding rule of Gavish and Donoho (2014) is used (see Details, References).
`center`	logical; center `data` so that its column-means are 0? Defaults to `TRUE`
`knots`	number of knots to use or the vectors of knots; defaults to 35
`p`	integer; the degree of B-splines functions to use
`m`	integer; the order of difference penalty to use
`lambda`	smoothing parameter; if not specified smoothing parameter is chosen using `stats::optim()` or a grid search
`alpha`	numeric; tuning parameter for GCV; see parameter `gamma` in `mgcv::gam()`
`search.grid`	logical; should a grid search be used to find `lambda`? Otherwise, `stats::optim()` is used
`search.length`	integer; length of grid to use for grid search for `lambda`; ignored if `search.grid` is `FALSE`
`method`	method to use; see `stats::optim()`
`lower`	see `stats::optim()`
`upper`	see `stats::optim()`
`control`	see `stats::optim()`

Value

A list with components

Yhat - If Y.pred is specified, the smooth version of Y.pred. Otherwise, if Y.pred=NULL, the smooth version of data.
scores - matrix of scores
mu - mean function
npc - number of principal components
efunctions - matrix of eigenvectors
evalues - vector of eigenvalues

Author(s)

Luo Xiao

References

Xiao, L., Li, Y., and Ruppert, D. (2013). Fast bivariate P-splines: the sandwich smoother, Journal of the Royal Statistical Society: Series B, 75(3), 577-599.

Xiao, L., Ruppert, D., Zipunnikov, V., and Crainiceanu, C. (2016). Fast covariance estimation for high-dimensional functional data. Statistics and Computing, 26, 409-421. DOI: 10.1007/s11222-014-9485-x.

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