Curve Registration for Exponential Family Functional Data
Simulate amplitude variance
Binary functional principal components analysis
Internal main preparation function for bfpca
Internal main optimization for bfpca
Nth derivative of spline basis
Coarsen an index vector to a given resolution
Define constraints for optimization of warping functions
Covariance estimation after Hall et al. (2008)
Crossproduct computation for highly irregular grids
Crossproduct computation for mostly regular grids
Convert data to a refund object
Estimate the derivative of the logit function
Determine the number of FPCs based on the share of explained variance
Correct slightly improper parameter vectors
Calculate expected score and score variance for the current subject.
Estimate variational parameter for the current subject.
Functional principal components analysis via variational EM
Internal main preparation function for fpca_gauss
Internal main optimization for fpca_gauss
Generalized functional principal component analysis
Generate subject-specific grid (t_star)
Create initial parameters for (inverse) warping functions
Apply lambda transformation of variational parameter.
Loss function for registration step optimization
Gradient of loss function for registration step
Simulate mean curve
Simulate mean
Create two-parameter piecewise linear (inverse) warping functions
Plot the results of a functional PCA
Simulate PC1
Simulate PC2
Register curves using constrained optimization and GFPCA
Register Exponential Family Functional Data
Internal function to register one curve
Simulate functional data
Simulate unregistered curves
Calculate quadratic form of spline basis functions for the current sub...
A method for performing joint registration and functional principal component analysis for curves (functional data) that are generated from exponential family distributions. This mainly implements the algorithms described in 'Wrobel et al. (2019)' <doi:10.1111/biom.12963> and further adapts them to potentially incomplete curves where (some) curves are not observed from the beginning and/or until the end of the common domain. Curve registration can be used to better understand patterns in functional data by separating curves into phase and amplitude variability. This software handles both binary and continuous functional data, and is especially applicable in accelerometry and wearable technology.