pca.ct {ctmva}

Continuous-time principal component analysis

Description

A continuous-time version of principal component analysis.

Usage

pca.ct(fdobj, cor = FALSE, common_trend = FALSE)

Arguments

fdobj

continuous-time multivariate data set of class "fd"

cor

logical: use correlation matrix if TRUE, covariance if FALSE (the default)

common_trend

logical: Should the curves be centered with respect to the mean function? Defaults to FALSE.

Value

Returns a list including:

var

variances of the principal components.

loadings

the matrix of loadings (i.e., its columns are the eigenvectors of the continuous-time covariance).

scorefd

score functions.

Author(s)

Biplab Paul <[e-mail]> and Philip Tzvi Reiss <[e-mail]>

See Also

cov.ct; princomp, for the classical version

Examples

## Not run: 

# Data for one session from a classic EEG data set
require(fda)
require(eegkit)
data(eegdata)
data(eegcoord)
longdat <- subset(eegdata, subject=="co2a0000369" & trial==0)
widedat <- reshape(longdat, direction="wide", drop=c("subject","group","condition","trial"),
                 v.names="voltage",idvar="channel")

# Convert time series for 64 channels to a functional data object
bsb <- create.bspline.basis(c(0,255),nbasis=30)
fdo <- Data2fd(argvals=0:255, y=t(as.matrix(widedat[,-1])), basisobj=bsb)
plot(fdo)

# Now do PCA and display first loadings for 3 PC's,
# along with percent variance explained by each
pcc <- pca.ct(fdo)
pve <- 100*pcc$var/sum(pcc$var)
par(mfrow=c(1,3))
cidx <- match(widedat[,1],rownames(eegcoord))
eegspace(eegcoord[cidx,4:5],pcc$loadings[,1], colorlab="PC1 loadings",
         main=paste0(round(pve[1],0), "%"), mar=c(17,3,12,2), cex.main=2)
eegspace(eegcoord[cidx,4:5],pcc$loadings[,2], colorlab="PC2 loadings",
         main=paste0(round(pve[2],0), "%"), mar=c(17,3,12,2), cex.main=2)
eegspace(eegcoord[cidx,4:5],pcc$loadings[,3], colorlab="PC3 loadings",
         main=paste0(round(pve[3],0), "%"), mar=c(17,3,12,2), cex.main=2)

# Linear discriminant analysis: discriminating among the 1st, 2nd and 3rd portions
#  of the time interval
ld <- lda.ct(fdo, c(85,170))
plot(ld)
eegspace(eegcoord[cidx,4:5],ld$scaling[,1], colorlab="LD1 coefficients",
         mar=c(17,3,12,2), cex.main=2)
eegspace(eegcoord[cidx,4:5],ld$scaling[,2], colorlab="LD2 coefficients",
         mar=c(17,3,12,2), cex.main=2)


## End(Not run)