Compute the Karcher (Frechet) mean for a sample of closed curves in the
elastic metric. This optimises simultaneously over reparameterisations and
rotations of the parameter domain.
Usage
karcher.mean.closed(fdataobj, max.iter = 15, tol = 1e-04, lambda = 0)
Arguments
- fdataobj
An object of class 'fdata' containing closed curves.
- max.iter
Maximum number of iterations (default 15).
- tol
Convergence tolerance (default 1e-4).
- lambda
Regularisation parameter controlling warping smoothness
(default 0).
Value
An object of class 'karcher.mean' with components:
- mean
fdata of the Karcher mean curve
- mean_srsf
numeric vector of the mean SRSF
- aligned
fdata of aligned curves
- gammas
fdata of warping functions
- n.iter
number of iterations used
- converged
logical indicating convergence
- fdataobj
the original fdata input
References
Srivastava, A. and Klassen, E. (2016). Functional and Shape Data
Analysis. Springer.
Examples
# \donttest{
set.seed(1)
t <- seq(0, 1, length.out = 100)
X <- matrix(0, 10, 100)
for (i in 1:10) X[i, ] <- sin(2 * pi * t + runif(1, -0.3, 0.3))
fd <- fdata(X, argvals = t)
km <- karcher.mean.closed(fd)
# }