fda (version 1.2.3)

register.fd: Register Functional Data Objects Using a Continuous Criterion

Description

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

register.fd(y0fd=NULL, yfd=NULL, WfdParobj=c(Lfdobj=2, lambda=1),
            conv=1e-04, iterlim=20, dbglev=1, periodic=FALSE, crit=2)

Arguments

y0fd

a functional data object defining the target for registration.

If yfd is NULL and y0fd is a multivariate data object, then y0fd is assigned to yfd and y0fd is replaced by its mean.

Alternatively, if yfd is a multiva

yfd

a multivariate functional data object defining the functions to be registered to target y0fd. If it is NULL and y0fd is a multivariate functional data object, yfd takes the value of y0fd.

WfdParobj

a functional parameter object for a single function. This is used as the initial value in the estimation of a function $W(t)$ that defines the warping function $h(t)$ that registers a particular curve. The object also contains information on

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. (If this is run with output buffering such as used with S-Plus, it may be neces

periodic

a logical variable: if TRUE, 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,

Value

• a named list of length 3 containing the following components:
• regfd
  A functional data object containing the registered functions.
• Wfd
  A functional data object containing the functions $h W(t)$ that define the warping functions $h(t)$.
• shift
  If the functions are periodic, this is a vector of time shifts.

source

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York. Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York, ch. 6 & 7.

Details

The warping function that smoothly and monotonely transforms the argument is defined by Wfd is the same as that defines the monotone smoothing function in for function smooth.monotone. See the help file for that function for further details.

See Also

smooth.monotone, smooth.morph

Examples

#See the analyses of the growth data for examples.
##
## 1.  Simplest call
##
# Specify smoothing weight 
lambda.gr2.3 <- .03

# Specify what to smooth, namely the rate of change of curvature
Lfdobj.growth    <- 2 

# Establish a B-spline basis
nage <- length(growth$age)
norder.growth <- 6
nbasis.growth <- nage + norder.growth - 2
rng.growth <- range(growth$age)
# 1 18 
wbasis.growth <- create.bspline.basis(rangeval=rng.growth,
                   nbasis=nbasis.growth, norder=norder.growth,
                   breaks=growth$age)

# Smooth consistent with the analysis of these data
# in afda-ch06.R, and register to individual smooths:  
cvec0.growth <- matrix(0,nbasis.growth,1)
Wfd0.growth  <- fd(cvec0.growth, wbasis.growth)
growfdPar2.3 <- fdPar(Wfd0.growth, Lfdobj.growth, lambda.gr2.3)
# Create a functional data object for all the boys
hgtmfd.all <- with(growth, smooth.basis(age, hgtm, growfdPar2.3))

nBoys <- 2
# nBoys <- dim(growth[["hgtm"]])[2]
# register.fd takes time, so use only 2 curves as an illustration
# to minimize compute time in this example;  

#Alternative to subsetting later is to subset now:  
#hgtmfd.all<-with(growth,smooth.basis(age, hgtm[,1:nBoys],growfdPar2.3))

# Register the growth velocity rather than the
# growth curves directly 
smBv <- deriv(hgtmfd.all$fd, 1)

# This takes time, so limit the number of curves registered to nBoys

smB.reg.0 <- register.fd(smBv[1:nBoys])

smB.reg.1 <- register.fd(smBv[1:nBoys],WfdParobj=c(Lfdobj=Lfdobj.growth, lambda=lambda.gr2.3))

##
## 2.  Call providing the target
##

smBv.mean <- deriv(mean(hgtmfd.all$fd[1:nBoys]), 1)
smB.reg.2a <- register.fd(smBv.mean, smBv[1:nBoys],
               WfdParobj=c(Lfdobj=Lfdobj.growth, lambda=lambda.gr2.3))

smBv.mean <- mean(smBv[1:nBoys]) 
smB.reg.2 <- register.fd(smBv.mean, smBv[1:nBoys],
               WfdParobj=c(Lfdobj=Lfdobj.growth, lambda=lambda.gr2.3))
all.equal(smB.reg.1, smB.reg.2) 

##
## 3.  Call using WfdParobj
##

# Create a dummy functional data object
# to hold the functional data objects for the
# time warping function
# ... start with a zero matrix (nbasis.growth, nBoys) 
smBc0 <- matrix(0, nbasis.growth, nBoys)
# ... convert to a functional data object 
smBwfd0 <- fd(smBc0, wbasis.growth)
# ... convert to a functional parameter object 
smB.wfdPar <- fdPar(smBwfd0, Lfdobj.growth, lambda.gr2.3)

smB.reg.3<- register.fd(smBv[1:nBoys], WfdParobj=smB.wfdPar)
all.equal(smB.reg.1, smB.reg.3)