fpca_gauss: Functional principal components analysis via variational EM
In julia-wrobel/registr: Curve Registration for Exponential Family Functional Data

Description Usage Arguments Value Author(s) References Examples

Function used in the FPCA step for registering functional data, called by register_fpca when family = "gaussian". Parameters estimated based on probabilistic PCA framework originally introduced by Tipping and Bishop in 1999.

The number of functional principal components (FPCs) can either be specified directly (argument npc) or chosen based on the explained share of variance (npc_varExplained). In the latter case, the explained share of variance and accordingly the number of FPCs is estimated before the main estimation step by once running the FPCA with npc = 20 (and correspondingly Kt = 20). Doing so, we approximate the overall variance in the data Y with the variance represented by the FPC basis with 20 FPCs.

fpca_gauss(
  Y,
  npc = NULL,
  npc_varExplained = NULL,
  Kt = 8,
  maxiter = 20,
  t_min = NULL,
  t_max = NULL,
  print.iter = FALSE,
  row_obj = NULL,
  seed = 1988,
  periodic = FALSE,
  error_thresh = 1e-04,
  subsample = TRUE,
  verbose = 1,
  ...
)

`Y`	Dataframe. Should have variables id, value, index.
`npc, npc_varExplained`	The number of functional principal components (FPCs) has to be specified either directly as `npc` or based on their explained share of variance. In the latter case, `npc_varExplained` has to be set to a share between 0 and 1.
`Kt`	Number of B-spline basis functions used to estimate mean functions and functional principal components. Default is 8. If `npc_varExplained` is used, `Kt` is set to 20.
`maxiter`	Maximum number of iterations to perform for EM algorithm. Default is 50.
`t_min`	Minimum value to be evaluated on the time domain.
`t_max`	Maximum value to be evaluated on the time domain.
`print.iter`	Prints current error and iteration
`row_obj`	If NULL, the function cleans the data and calculates row indices. Keep this NULL if you are using standalone `register` function.
`seed`	Set seed for reproducibility. Defaults to 1988.
`periodic`	If TRUE, uses periodic b-spline basis functions. Default is FALSE.
`error_thresh`	Error threshold to end iterations. Defaults to 0.0001.
`subsample`	if the number of rows of the data is greater than 10 million rows, the 'id' values are subsampled to get the mean coefficients.
`verbose`	Can be set to integers between 0 and 4 to control the level of detail of the printed diagnostic messages. Higher numbers lead to more detailed messages. Defaults to 1.
`...`	Additional arguments passed to or from other functions

An object of class fpca containing:

`fpca_type`	Information that FPCA was performed with the 'variationEM' approach, in contrast to registr::gfpca_twoStep.
`t_vec`	Time vector over which the mean `mu` and the functional principal components `efunctions` were evaluated.
`knots`	Cutpoints for B-spline basis used to rebuild `alpha`.
`efunctions`	D \times npc matrix of estimated FPC basis functions.
`evalues`	Estimated variance of the FPC scores.
`evalues_sum`	Approximation of the overall variance in `Y`, based on an initial run of the FPCA with `npc = 20`. Is `NULL` if `npc_varExplained` was not specified.
`npc`	number of FPCs.
`scores`	I \times npc matrix of estimated FPC scores.
`alpha`	Estimated population-level mean.
`mu`	Estimated population-level mean. Same value as `alpha` but included for compatibility with `refund.shiny` package.
`subject_coefs`	B-spline basis coefficients used to construct subject-specific means. For use in `registr()` function.
`Yhat`	FPC approximation of subject-specific means.
`Y`	The observed data.
`family`	`gaussian`, for compatibility with `refund.shiny` package.
`sigma2`	Estimated error variance

Julia Wrobel julia.wrobel@cuanschutz.edu, Jeff Goldsmith ajg2202@cumc.columbia.edu, Alexander Bauer alexander.bauer@stat.uni-muenchen.de

Tipping, M. E. and Bishop, C (1999). Probabilistic Principal Component Analysis. Journal of the Royal Statistical Society Series B,, 592–598.

data(growth_incomplete)

# estimate 2 FPCs
fpca_obj = fpca_gauss(Y = growth_incomplete, npc = 2)
plot(fpca_obj)

# estimate npc adaptively, to explain 90% of the overall variation

fpca_obj2 = fpca_gauss(Y = growth_incomplete, npc_varExplained = 0.9)
plot(fpca_obj, plot_FPCs = 1:2)