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Trimmed Karcher Mean in Elastic Metric

Source: R/alignment.R
robust.karcher.mean.Rd

Compute a robust version of the Karcher mean by iteratively trimming the most distant curves before updating the mean estimate. This reduces the influence of outlying observations on the mean shape.

Usage

robust.karcher.mean(
  fdataobj,
  trim = 0.1,
  max.iter = 20,
  tol = 1e-04,
  lambda = 0
)

Arguments

fdataobj

An object of class 'fdata'.

trim

Fraction of most distant curves to trim at each iteration (default 0.1).

max.iter

Maximum number of iterations (default 20).

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 trimmed 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

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.

See also

karcher.mean, karcher.median

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)
rkm <- robust.karcher.mean(fd, trim = 0.1)
# }