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Karcher Median in Elastic Metric

Source: R/alignment.R
karcher.median.Rd

Compute the Karcher median of functional data in the elastic metric using the Weiszfeld algorithm. The Karcher median minimises the sum of distances rather than the sum of squared distances, making it more robust to outliers than the Karcher mean.

Usage

karcher.median(fdataobj, max.iter = 30, tol = 1e-04, lambda = 0, trim = 0)

Arguments

fdataobj

An object of class 'fdata'.

max.iter

Maximum number of Weiszfeld iterations (default 30).

tol

Convergence tolerance (default 1e-4).

lambda

Regularisation parameter controlling warping smoothness (default 0).

trim

Fraction of most distant curves to trim before aggregation (default 0, no trimming).

Value

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

median

fdata of the Karcher median curve

median_srsf

numeric vector of the median 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

Fletcher, P.T., Venkatasubramanian, S., and Joshi, S. (2009). The geometric median on Riemannian manifolds with application to robust atlas estimation. NeuroImage, 45(1):S143–S152.

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

See also

karcher.mean, robust.karcher.mean

Examples

# \donttest{
set.seed(1)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 15, 50)
for (i in 1:15) X[i, ] <- sin(2 * pi * t + runif(1, -0.3, 0.3))
fd <- fdata(X, argvals = t)
km <- karcher.median(fd)
# }