Joint Amplitude-Phase Gaussian Generative Model

Fit a joint Gaussian generative model that captures both amplitude and phase variability. Unlike gauss.model which models amplitude only, this model jointly models the amplitude and warping components, allowing generated curves to exhibit realistic phase variability.

Usage

joint.gauss.model(
  karcher,
  n.components = 3,
  n.samples = 50,
  balance = 1,
  seed = 42
)

Arguments

karcher: An object of class 'karcher.mean' (result of karcher.mean).
n.components: Number of principal components to retain (default 3).
n.samples: Number of random curves to generate (default 50).
balance: Balance parameter controlling the relative weight of amplitude and phase components (default 1.0).
seed: Random seed for reproducibility (default 42).

Value

A list with components:

samples: fdata of generated random curves
eigenvalues: numeric vector of eigenvalues
eigenfunctions: matrix of eigenfunctions
scores: matrix of joint PCA scores

References

Tucker, J.D., Wu, W., and Srivastava, A. (2013). Generative models for functional data using phase and amplitude separation. Computational Statistics & Data Analysis, 61:50–66.

Examples

# \donttest{
set.seed(1)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 20, 50)
for (i in 1:20) X[i, ] <- sin(2 * pi * t + runif(1, -0.3, 0.3))
fd <- fdata(X, argvals = t)
km <- karcher.mean(fd)
jgm <- joint.gauss.model(km, n.components = 2, n.samples = 10)
# }