flipFuns {funData}

Flip functional data objects

Description

This function flips an object newObject of class funData, irregFunData or multiFunData with respect to a reference object refObject of the same class (or of class funData, if newObject is irregular). This is particularly useful when dealing with functional principal components, as they are only defined up to a sign change. For details, see below.

Usage

flipFuns(refObject, newObject, ...)

Arguments

refObject

An object of class funData, irregFunData or multiFunData that serves as reference. It must have the same number of observations as newObject or have only one observation. In this case, all observations in newObject are flipped with respect to this single observation.

newObject

An object of class funData, irregFunData or multiFunData that is to be flipped with respect to refObject.

...

Further parameters passed to norm.

Details

Functional principal component analysis is an important tool in functional data analysis. Just as eigenvectors, eigenfunctions (or functional principal components) are only defined up to a sign change. This may lead to difficulties in simulation studies or when bootstrapping pointwise confidence bands, as in these cases one wants the estimates to have the same "orientation" as the true function (in simulation settings) or the non-bootstrapped estimate (when calculating bootstrap confidence bands). This function allows to flip (i.e. multiply by -1) all observations in newObject that have a different orientation than their counterparts in refData.

Technically, the function compares the distance between newObject and refObject

|||f_\mathrm{new} - f_\mathrm{ref}|||

and the distance between newObject and -1 * refObject

|||f_\mathrm{new} + f_\mathrm{ref}|||.

If newObject is closer to -1 * refObject, it is flipped, i.e. multiplied by -1.

Value

An object of the same class as newData with flipped observations.

Warning

The function is currently implemented only for functional data with one- and two-dimensional domains.

See Also

funData, irregFunData, multiFunData, Arith.funData

Examples

### Univariate
argvals <- seq(0,2*pi,0.01)
refData <- funData(argvals, rbind(sin(argvals))) # one observation as reference
newData <- funData(argvals, outer(sample(c(-1,1), 11, replace = TRUE) * seq(0.75, 1.25, by = 0.05),
                               sin(argvals)))

oldpar <- par(no.readonly = TRUE)
par(mfrow = c(1,2))

plot(newData, col = "grey", main = "Original data")
plot(refData, col = "red", lwd = 2, add = TRUE)

plot(flipFuns(refData, newData), col = "grey", main = "Flipped data")
plot(refData, col = "red", lwd = 2, add = TRUE)

### Univariate (irregular)
ind <- replicate(11, sort(sample(1:length(argvals), sample(5:10,1)))) # sample observation points
argvalsIrreg <- lapply(ind, function(i){argvals[i]})
argvalsIrregAll <- unique(sort(unlist(argvalsIrreg)))
 # one observation as reference (fully observed)
refDataFull <- funData(argvals, rbind(sin(argvals)))
 # one observation as reference (irregularly observed)
refDataIrreg <- irregFunData(argvals = list(argvalsIrregAll), X = list(sin(argvalsIrregAll)))
newData <- irregFunData(argvals = argvalsIrreg, X = mapply(function(x, a, s){s * a * sin(x)},
     x = argvalsIrreg, a = seq(0.75, 1.25, by = 0.05), s = sample(c(-1,1), 11, replace = TRUE)))

plot(newData, col = "grey", main = "Original data (regular reference)")
plot(refDataFull, col = "red", lwd = 2, add = TRUE)

plot(flipFuns(refDataFull, newData), col = "grey", main = "Flipped data")
plot(refDataFull, col = "red", lwd = 2, add = TRUE)

plot(newData, col = "grey", main = "Original data (irregular reference)")
plot(refDataIrreg, col = "red", lwd = 2, add = TRUE)

plot(flipFuns(refDataIrreg, newData), col = "grey", main = "Flipped data")
plot(refDataIrreg, col = "red", lwd = 2, add = TRUE)

### Multivariate
refData <- multiFunData(funData(argvals, rbind(sin(argvals))), # one observation as reference
                        funData(argvals, rbind(cos(argvals)))) 
sig <- sample(c(-1,1), 11, replace = TRUE) 
newData <- multiFunData(funData(argvals, outer(sig * seq(0.75, 1.25, by = 0.05), sin(argvals))),
                        funData(argvals, outer(sig * seq(0.75, 1.25, by = 0.05), cos(argvals))))
                        
par(mfrow = c(2,2))

plot(newData[[1]], col = topo.colors(11), main = "Original data")
plot(refData[[1]], col = "red", lwd = 2, add = TRUE)

plot(newData[[2]], col = topo.colors(11), main = "Original data")
plot(refData[[2]], col = "red", lwd = 2, add = TRUE)

plot(flipFuns(refData, newData)[[1]], col = topo.colors(11), main = "Flipped data")
plot(refData[[1]], col = "red", lwd = 2, add = TRUE)

plot(flipFuns(refData, newData)[[2]], col = topo.colors(11), main = "Flipped data")
plot(refData[[2]], col = "red", lwd = 2, add = TRUE)

par(oldpar)