Multivariate functional pca

Description

This function will run a weighted functional pca in the two cases of uni, and multivariate cases. If the observations (the curves) are given with weights, set up the parameter tik.

Usage

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  mfpca(fd, nharm, tik = numeric(0))

Arguments

fd

in the univariate case fd is an object from a class fd. Otherwise in the multivariate case fd is a list of fd object (fd=list(fd1,fd2,..)).

nharm

number of harmonics or principal component to be retain.

tik

the weights of the functional pca which corresponds to the weights of the curves. If don't given, then we will run a classic functional pca (without weighting the curves).

Value

When univarite functional data, the function are returning an object of calss "pca.fd", When multivariate a list of "pca.fd" object by dimension. The "pca.fd" class contains the folowing parameter: harmonics: functional data object storing the eigen function values: the eigenvalues varprop: the normalized eigenvalues (eigenvalues divide by their sum) scores: the scores matrix meanfd: the mean of the functional data object

Examples

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data(growth)
data=cbind(matrix(growth$hgtm,31,39),matrix(growth$hgtf,31,54));
t=growth$age;
splines <- create.bspline.basis(rangeval=c(1, max(t)), nbasis = 20,norder=4);
fd <- Data2fd(data, argvals=t, basisobj=splines);
pca=mfpca(fd,nharm=2)
summary(pca)