multiple_align_multivariate {fdasrvf} | R Documentation |
Group-wise multivariate function alignment to specified mean
Description
This function aligns a collection of functions using the elastic square-root velocity (srvf) framework.
Usage
multiple_align_multivariate(
beta,
mu,
mode = "O",
alignment = TRUE,
rotation = FALSE,
scale = FALSE,
lambda = 0,
ncores = 1L,
verbose = TRUE
)
Arguments
beta |
A numeric array of shape |
mu |
array of size |
mode |
A character string specifying whether the input curves should be
considered open ( |
alignment |
A boolean value specifying whether the curves should be
aligned before computing the distance matrix. Defaults to |
rotation |
A boolean specifying whether the distance should be made
invariant by rotation. Defaults to |
scale |
A boolean specifying whether the distance should be made
invariant by scaling. This is effectively achieved by making SRVFs having
unit length and switching to an appropriate metric on the sphere between
normalized SRVFs. Defaults to |
lambda |
A numeric value specifying the weight of a penalty term that
constraints the warping function to be not too far from the identity.
Defaults to |
ncores |
An integer value specifying the number of cores to use for
parallel computation. Defaults to |
verbose |
verbose printing (default TRUE) |
Value
Returns a fdacurve object containing:
-
beta
: A numeric array of shapeL \times M \times N
storing the original input data. -
q
: A numeric array of shapeL \times M \times N
storing the SRVFs of the input data. -
betan
: A numeric array of shapeL \times M \times N
storing the aligned, possibly optimally rotated and optimally scaled, input data. -
qn
: A numeric array of shapeL \times M \times N
storing the SRVFs of the aligned, possibly optimally rotated and optimally scaled, input data. -
gamma
: A numeric array of shapeL \times M \times N
storing the warping functions of the aligned, possibly optimally rotated and optimally scaled, input data. -
R
: A numeric array of shapeL \times L \times N
storing the rotation matrices of the aligned, possibly optimally rotated and optimally scaled, input data. -
betamean
: A numeric array of shapeL \times M
storing the Karcher mean or median of the input data. -
qmean
: A numeric array of shapeL \times M
storing the Karcher mean or median of the SRVFs of the input data. -
type
: A character string indicating whether the Karcher mean or median has been returned. -
E
: A numeric vector storing the energy of the Karcher mean or median at each iteration. -
qun
: A numeric vector storing the cost function of the Karcher mean or median at each iteration.
References
Srivastava, A., Klassen, E., Joshi, S., Jermyn, I., (2011). Shape analysis of elastic curves in euclidean spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33 (7), 1415-1428.