Registration of Functional Observations Using Landmarks
Registration of Functional Observations Using Landmarks
DESCRIPTION:
It is common to see that among a set of functions certain prominent
features such peaks and valleys, called landmarks, do not occur
at the same times, or other
argument values. This is called phase variation, and it can be
essential to align these features before proceeding with further
functional data analyses. This function uses the timings of these
features to align or register the curves. The registration involves
estimating a nonlinear transformation of the argument continuum for each
functional observation. This transformation is called a warping
function. It must be strictly increasing and smooth.
USAGE:
landmarkreg(fd, fd0, ximarks, x0marks=xmeanmarks, wbasis=basis, Lfd=0, sparval=1e-010, monwrd=F)
REQUIRED ARGUMENTS:
- fd
-
A functional data object containing the curves to be registered.
- fd0
-
A functional data object with a single observation defining a template
or gold standard function to which the other functions are registered.
- ximarks
-
A matrix containing the timings or argument values associated with the
landmarks for the observations in fd to be registered. The
number of rows
equals the number of observations, and the number of columns equals the
number of landmarks.
OPTIONAL ARGUMENTS:
- x0marks
-
A vector containing the timings or argument values associated with the
landmarks for the template or gold standard function in
fd0.
- wbasis
-
A basis object used to define the warping functions.
- Lfd
-
Either a nonnegative integer of a linear differential operator to
be applied to the functions before registering them.
- sparval
-
A smoothing parameter controlling the smoothness of the estimated
warping functions.
- monwrd
-
If TRUE, the warping function is estimated using a monotone
smoothing methhod; otherwise, a regular smoothing method is used,
which is not guaranteed to give strictly monotonic warping
functions.
VALUE:
A list with these entries is returned.
- "fdreg"
a functional data object for the registered curves
- "warpfd"
A functional data object for the warping functions
DETAILS:
It is essential that the location of every landmark be clearly
defined
in each of the curves as well as the template function. If this is not
the case, consider using the continuous registration function
register.fd.
Although requiring that a monotone smoother be used to estimate the
warping functions is safer, it adds considerably to the computatation
time since monotone smoothing is itself an iterative process. It is
usually better to try an initial registration with this feature to see
if there are any failures of monotonicity. Moreover, monotonicity
failures can usually be cured by increasing the smoothing parameter
sparval.
Not much curvature is usually required in the warping functions, so
a rather low power basis, usually B-splines, is suitable for
argument wbasis.
A registration with a few prominent landmarks is often a good
preliminary to using the more sophisticated but more lengthy process in
register.fd.
REFERENCES:
Ramsay, J. O. and Silverman, B. W. (1997) Functional Data
Analysis. New York: Springer. Registration is
described in Chapter 5.
SEE ALSO:
register.fd
EXAMPLES: