Functional Principal Components Analysis
pca.fd
Language Reference for FDA Library

Functional Principal Components Analysis

DESCRIPTION:

Functional Principal components analysis aims to display types of variation across a sample of functions. Principal components analysis is an exploratory data analysis that tends to be an early part of many projects. These modes of variation are called principal components or harmonics. This function computes these harmonics, the eigenvalues that indicate how important each mode of variation, and harmonic scores for individual functions. If the functions are multivariate, these harmonics are combined into a composite function that summarizes joint variation among the several functions that make up a multivariate functional observation.

USAGE:

pca.fd(fdobj, nharm = 2, harmfdPar=fdPar(),
       centerfns = T)

REQUIRED ARGUMENTS:

fdobj
a functional data object.

OPTIONAL ARGUMENTS:

nharm
the number of harmonics or principal components to compute.
harmfdPar
a functional parameter object that defines the harmonic or principal component functions to be estimated.
centerfns
a logical value: if T, subtract the mean function from each function before computing principal components.

VALUE:

an object of class "pca.fd" with these named entries:
harmonics
a functional data object for the harmonics or eigenfunctions
values
the complete set of eigenvalues
scores
s matrix of scores on the principal components or harmonics
varprop
a vector giving the proportion of variance explained by each eigenfunction
meanfd
a functional data object giving the mean function

SEE ALSO:

cca.fd, pda.fd

EXAMPLES:

#  carry out a PCA of temperature
#  penalize harmonic acceleration, use varimax rotation
harmfdPar     <- fdPar(daybasis65, harmaccelLfd, 1e5)
daytemppcaobj <- pca.fd(daytempfd, nharm=4, harmfdPar)
daytemppcaobj <- varmx.pca.fd(daytemppcaobj)
#  plot harmonics
plot.pca.fd(daytemppcaobj, cex=1.2)