ggtaugplot: Augmentation plot for each mode of an object of class taug...

In tensorBSS: Blind Source Separation Methods for Tensor-Valued Observations

Augmentation plot for each mode of an object of class taug using ggplot2

Description

The augmentation plot is a measure for deciding about the number of interesting components. Of interest for the augmentation plot, which is quite similar to the ladle plot, is the minimum. The function offers, however, also the possibility to plot other criterion values that combined make up the actual criterion.

Usage

ggtaugplot(x, crit = "gn", type = "l", scales = "free", position = "horizontal",
  ylab = crit, xlab = "component", main = deparse(substitute(x)),  ...)

Arguments

x	an object of class taug.
crit	the criterion to be plotted, options are "gn", "fn", "phin" and "lambda".
type	plotting type, either lines l or points p.
position	placement of augmentation plots for separate modes, options are "horizontal" and "vertical".
scales	determines whether the x- and y-axis scales are shared or allowed to vary freely across the subplots. The options are: both axes are free (the default, "free"), x-axis is free ("free_x"), y-axis is free ("free_y"), neither is free ("fixed").
ylab	default ylab value.
xlab	default xlab value.
main	default title.
...	other arguments for the plotting functions.

Details

The main criterion of the augmentation criterion is the scaled sum of the eigenvalues and the measure of variation of the eigenvectors up to the component of interest.

The sum is denoted "gn" and the individual parts are "fn" for the measure of the eigenvector variation and "phin" for the scaled eigenvalues. The last option "lambda" corresponds to the unscaled eigenvalues yielding then a screeplot.

The plot is drawn separately for each mode of the data.

Author(s)

Klaus Nordhausen, Joni Virta, Una Radojicic

References

Radojicic, U., Lietzen, N., Nordhausen, K. and Virta, J. (2021), On order determinaton in 2D PCA. Manuscript.

See Also

tPCAaug

Examples

library(ICtest)


# matrix-variate example
n <- 200
sig <- 0.6

Z <- rbind(sqrt(0.7)*rt(n,df=5)*sqrt(3/5),
           sqrt(0.3)*runif(n,-sqrt(3),sqrt(3)),
           sqrt(0.3)*(rchisq(n,df=3)-3)/sqrt(6),
           sqrt(0.9)*(rexp(n)-1),
           sqrt(0.1)*rlogis(n,0,sqrt(3)/pi),
           sqrt(0.5)*(rbeta(n,2,2)-0.5)*sqrt(20)
)

dim(Z) <- c(3, 2, n)

U1 <- rorth(12)[,1:3]
U2 <- rorth(8)[,1:2]
U <- list(U1=U1, U2=U2)
Y <- tensorTransform2(Z,U,1:2)
EPS <- array(rnorm(12*8*n, mean=0, sd=sig), dim=c(12,8,n))
X <- Y + EPS


TEST <- tPCAaug(X)
TEST
ggtaugplot(TEST)

# higher order tensor example

Z2 <- rnorm(n*3*2*4*6)

dim(Z2) <- c(3,2,4,6,n)

U2.1 <- rorth(10)[ ,1:3]
U2.2 <- rorth(8)[ ,1:2]
U2.3 <- rorth(5)[ ,1:4]
U2.4 <- rorth(15)[ ,1:6]

U2 <- list(U1 = U2.1, U2 = U2.2, U3 = U2.3, U4 = U2.4)
Y2 <- tensorTransform2(Z2, U2, 1:4)
EPS2 <- array(rnorm(10*8*5*15*n, mean=0, sd=sig), dim=c(10, 8, 5, 15, n))
X2 <- Y2 + EPS2


TEST2 <- tPCAaug(X2)
ggtaugplot(TEST2, crit = "lambda", position = "vertical",
 scales = "free_x")

tensorBSS documentation built on Sept. 12, 2024, 5:07 p.m.