Functions for mapping aligned functional data to a tangent space
on the Hilbert sphere, enabling standard linear operations (PCA,
regression) on elastically aligned curves.
TSRVF Transform
Usage
tsrvf.transform(fdataobj, max.iter = 20, tol = 1e-04, lambda = 0)
Arguments
- fdataobj
An object of class 'fdata'.
- max.iter
Maximum number of Karcher mean iterations. Default 20.
- tol
Convergence tolerance for Karcher mean. Default 1e-4.
- lambda
Penalty weight on warp deviation from identity. Default 0.
Value
An object of class 'tsrvf' with components:
- tangent_vectors
fdata of tangent vectors in Euclidean space
- mean
fdata of the Karcher mean curve
- gammas
fdata of warping functions
- converged
logical indicating Karcher mean convergence
- fdataobj
the original input
Details
Compute the TSRVF (Transported SRSF) representation of functional data.
This performs Karcher mean alignment and then maps the aligned SRSFs
to the tangent space at the mean via the inverse exponential map.
References
Su, J., Kurtek, S., Klassen, E., and Srivastava, A. (2014).
Statistical analysis of trajectories on Riemannian manifolds:
bird migration, hurricane tracking and video surveillance.
Annals of Applied Statistics, 8(1):530–552.
Examples
# \donttest{
fd <- fdata(matrix(rnorm(200), 20, 10), argvals = seq(0, 1, length.out = 10))
tv <- tsrvf.transform(fd, max.iter = 5)
# }