Shape Mean (Karcher Mean in Quotient Space)

Compute the Karcher (Frechet) mean of functional data in a shape quotient space. This simultaneously estimates the mean shape and aligns all curves, factoring out the specified nuisance transformations.

Usage

shape.mean(
  fdataobj,
  quotient = c("reparameterization", "translation", "scale"),
  lambda = 0,
  max.iter = 20,
  tol = 1e-04
)

Arguments

fdataobj: An object of class fdata.
quotient: Character: the quotient space. One of "reparameterization", "translation", or "scale".
lambda: Regularization parameter (default 0).
max.iter: Maximum number of iterations (default 20).
tol: Convergence tolerance (default 1e-4).

Value

An object of class shape.mean with components:

mean: The shape mean curve (numeric vector)
mean.srsf: SRSF of the mean curve
gammas: Matrix of warping functions (n x m)
aligned.data: Matrix of aligned curves (n x m)
n.iter: Number of iterations
converged: Logical: did the algorithm converge?
fdataobj: Original fdata object
quotient: Quotient space used
call: The matched call

References

Srivastava, A. and Klassen, E. (2016). Functional and Shape Data Analysis. Springer.

Examples

# \donttest{
set.seed(1)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 10, 50)
for (i in 1:10) X[i, ] <- sin(2 * pi * (t - i / 50)) + rnorm(50, 0, 0.1)
fd <- fdata(X, argvals = t)
sm <- shape.mean(fd, quotient = "reparameterization", max.iter = 10)
sm
#> Shape Mean (Quotient Space)
#>   Curves: 10 x 50 grid points
#>   Quotient: reparameterization 
#>   Iterations: 10 
#>   Converged: FALSE 
# }