multivariate_karcher_mean {fdasrvf}

Karcher Mean of Multivariate Functional Data

Description

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

Usage

multivariate_karcher_mean(beta, lambda = 0, maxit = 20, ms = "mean")

Arguments

beta

L \times M \times N and it is interpreted as a sample of N L-dimensional curves observed on a grid of size M.

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

betamean

mean or median curve

type

string indicating whether mean or median is returned

betan

aligned curves

q

array of srvfs

qn

array of aligned srvfs

gam

array of warping functions

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