Gaussian Generative Model for Elastic Functional Data

Fit a Gaussian generative model to elastic functional data using PCA on the SRVF representations. The model captures amplitude variability and can generate new random curves from the estimated distribution.

Usage

gauss.model(karcher, n.components = 3, n.samples = 50, 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).
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 (components x grid)
scores: matrix of PCA scores (curves x components)

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)
gm <- gauss.model(km, n.components = 2, n.samples = 10)
# }