curve_karcher_mean: Karcher Mean of Curves

In fdasrvf: Elastic Functional Data Analysis

Karcher Mean of Curves

Description

Calculates Karcher mean or median of a collection of curves using the elastic square-root velocity (srvf) framework.

Usage

curve_karcher_mean(
  beta,
  mode = "O",
  rotated = T,
  scale = F,
  lambda = 0,
  maxit = 20,
  ms = "mean"
)

Arguments

beta	array (n,T,N) for N number of curves
mode	Open ("O") or Closed ("C") curves
rotated	Optimize over rotation (default = T)
scale	Include scale (default = F)
lambda	A numeric value specifying the elasticity. Defaults to 0.0.
maxit	maximum number of iterations
ms	string defining whether the Karcher mean ("mean") or Karcher median ("median") is returned (default = "mean")

Value

Returns a list containing

mu	mean srvf
beta	centered data
betamean	mean or median curve
type	string indicating whether mean or median is returned
v	shooting vectors
q	array of srvfs
gam	array of warping functions
cent	centers of original curves
len	length of curves
len_q	length of srvfs
mean_scale	mean length
mean_scale_q	mean length srvf
E	energy
qun	cost function

References

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

Examples

out <- curve_karcher_mean(beta[, , 1, 1:2], maxit = 2)
# note: use more shapes, small for speed

fdasrvf documentation built on Nov. 19, 2023, 1:09 a.m.