Register Functional Data Objects
Register Functional Data Objects
DESCRIPTION:
Curves are aligned with a target or template curve using a continuous
criterion. By aligned is meant that the shape of each curve is matched
as closely as possible to that of the target by means of a smooth
increasing transformation of the argument, or a warping function.
USAGE:
registerfd(y0fd, yfd, Wfd0, Lfdobj=2, lambda=1, conv=0.01, iterlim=10,
dbglev=1, periodic=0, crit=2)
REQUIRED ARGUMENTS:
- y0fd
-
A functional data object defining the target. It must be
univariate and it must define a single functional observation.
- yfd
-
A functional data object defining the functions to be registered to
yfd0.
- Wfd0
-
A functional data object defining the initial value of a function
W(t) that determines the warping function.
OPTIONAL ARGUMENTS:
- Lfdobj
-
Either a nonnegative integer or a linear differential operator object
that defines a rougness penalty to be applied to functional data object
Wfd0. If present, the derivative or the value of
applying the operator is evaluated rather than the functions themselves.
- lambda
-
A nonnegative smoothing parameter that controls the degree of roughness
in Wfdobj, and consequently in the monotone smoothing
function.
- conv
-
A criterion for convergence of the iterations.
- iterlim
-
A limit on the number of iterations.
- dbglev
-
Either 0, 1, or 2. This controls the amount information printed out on
each iteration, with 0 implying no output, 1 intermediate output level,
and 2 full output.
- periodic
-
A logical variable. If T, the functions are considered to be
periodic, in which case a constant can be added to all argument
values after they are warped.
- crit
-
An integer that is either 1 or 2 that indicates the nature of the
continuous registration criterion that is used. If 1, the criterion is
least squares, and if 2, the criterion is the minimum eigenvalue of a
cross-product matrix. In general, criterion 2 is to be preferred.
VALUE:
A list containing:
regstr <- list("regfd"=regfd, "Wfd"=Wfd, "shift"=shift)
- regfd
-
The registered versions of the original function defined in
yfd.
- Wfd
- The functional data object determining the warping functions.
- shift
- A constant that is added to the warped arguments if the data
are considered periodic. Otherwise, zero.
DETAILS:
The warping function that smoothly and monotonely transforms the
argument is defined by Wfd0 in the same that the monotone
smoothing function is for function smooth.monotone. See the
help file for that function for further details.
REFERENCES: