bfpca: Binary functional principal components analysis

In registr: Curve Registration for Exponential Family Functional Data

Binary functional principal components analysis

Description

Function used in the FPCA step for registering binary functional data, called by register_fpca when family = "binomial". This method uses a variational EM algorithm to estimate scores and principal components for binary functional data.

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.

Usage

bfpca(
  Y,
  npc = NULL,
  npc_varExplained = NULL,
  Kt = 8,
  maxiter = 50,
  t_min = NULL,
  t_max = NULL,
  print.iter = FALSE,
  row_obj = NULL,
  seed = 1988,
  periodic = FALSE,
  error_thresh = 1e-04,
  verbose = 1,
  subsample = TRUE,
  ...
)

Arguments

Y	Dataframe. Should have variables id, value, index.
npc	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.
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.
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.
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.
...	Additional arguments passed to or from other functions

Value

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, before applying the response function.
Y	The observed data.
family	binomial, for compatibility with refund.shiny package.
error	vector containing error for each iteration of the algorithm.

Author(s)

Julia Wrobel [e-mail], Jeff Goldsmith [e-mail], Alexander Bauer [e-mail]

References

Jaakkola, T. S. and Jordan, M. I. (1997). A variational approach to Bayesian logistic regression models and their extensions. Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics.

Tipping, M. E. (1999). Probabilistic Visualisation of High-dimensional binary data. Advances in neural information processing systems, 592–598.

Examples

Y = simulate_functional_data()$Y

# estimate 2 FPCs
bfpca_obj = bfpca(Y, npc = 2, print.iter = TRUE, maxiter = 25)



plot(bfpca_obj)

# estimate npc adaptively, to explain 90% of the overall variation
bfpca_obj2 = bfpca(Y, npc_varExplained = 0.9, print.iter = TRUE, maxiter = 30)
plot(bfpca_obj2)

registr documentation built on Oct. 3, 2022, 1:05 a.m.