cca.fd {fda}

Functional Canonical Correlation Analysis

Description

Carry out a functional canonical correlation analysis with regularization or roughness penalties on the estimated canonical variables.

Usage

cca.fd(fdobj1, fdobj2=fdobj1, ncan = 2,
       ccafdPar1=fdPar(basisobj1, 2, 1e-10),
       ccafdPar2=ccafdPar1, centerfns=TRUE)

Arguments

fdobj1

a functional data object.

fdobj2

a functional data object. By default this is fdobj1 , in which case the first argument must be a bivariate functional data object.

ncan

the number of canonical variables and weight functions to be computed. The default is 2.

ccafdPar1

a functional parameter object defining the first set of canonical weight functions. The object may contain specifications for a roughness penalty. The default is defined using the same basis as that used for fdobj1 with a slight penalty on its second derivative.

ccafdPar2

a functional parameter object defining the second set of canonical weight functions. The object may contain specifications for a roughness penalty. The default is ccafdParobj1 .

centerfns

if TRUE, the functions are centered prior to analysis. This is the default.

Value

an object of class cca.fd with the 5 slots:

ccwtfd1

a functional data object for the first canonical variate weight function

ccwtfd2

a functional data object for the second canonical variate weight function

cancorr

a vector of canonical correlations

ccavar1

a matrix of scores on the first canonical variable.

ccavar2

a matrix of scores on the second canonical variable.

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

plot.cca.fd, varmx.cca.fd, pca.fd

Examples

#  Canonical correlation analysis of knee-hip curves

gaittime  <- (1:20)/21
gaitrange <- c(0,1)
gaitbasis <- create.fourier.basis(gaitrange,21)
lambda    <- 10^(-11.5)
harmaccelLfd <- vec2Lfd(c(0, 0, (2*pi)^2, 0))

gaitfd    <- fda::fd(matrix(0,gaitbasis$nbasis,1), gaitbasis)
gaitfdPar <- fda::fdPar(gaitfd, harmaccelLfd, lambda)
gaitfd    <- fda::smooth.basis(gaittime, gait, gaitfdPar)$fd
ccafdPar  <- fda::fdPar(gaitfd, harmaccelLfd, 1e-8)
ccafd0    <- cca.fd(gaitfd[,1], gaitfd[,2], ncan=3, ccafdPar, ccafdPar)
#  display the canonical correlations
round(ccafd0$ccacorr[1:6],3)
#  compute a VARIMAX rotation of the canonical variables
ccafd <- varmx.cca.fd(ccafd0)
#  plot the canonical weight functions
oldpar <- par(no.readonly= TRUE)
plot.cca.fd(ccafd)
par(oldpar)