Karcher Mean in Elastic Metric

Compute the Karcher (Fréchet) mean of functional data in the elastic metric. This simultaneously estimates the mean shape and aligns all curves.

Usage

karcher.mean(
  fdataobj,
  max.iter = 20,
  tol = 1e-04,
  periodic = FALSE,
  rotate.method = "peak",
  rotate.args = list()
)

Arguments

fdataobj

An object of class 'fdata'.

max.iter

Maximum number of iterations (default 20).

tol

Convergence tolerance (default 1e-4).

periodic

Logical; if TRUE, circularly rotate each curve to a canonical position before computing the Karcher mean. See elastic.align for details. Default is FALSE.

rotate.method

Rotation method when periodic = TRUE: one of "peak" (default), "xcorr", "landmark", or "iterative". See periodic.rotate for details.

rotate.args

A named list of additional arguments passed to periodic.rotate (e.g., reference, landmark.func, max.iter).

Value

An object of class 'karcher.mean' with components:

mean

fdata of the Karcher mean curve

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

rotations

integer vector of circular rotation shifts applied (NULL when periodic = FALSE)

rotate_method

the rotation method used (NULL when periodic = FALSE)

References

Srivastava, A., Klassen, E., Joshi, S.H., and Jermyn, I.H. (2011). Shape analysis of elastic curves in Euclidean spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(7):1415–1428.

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{
fd <- fdata(matrix(rnorm(200), 20, 10), argvals = seq(0, 1, length.out = 10))
km <- karcher.mean(fd)
# }