residual.EM: Function to evaluate residual end-member loading.

Description

This function calculates the residual end-member loading. It uses the modelled end-member loadings as input and evaluates the root of 1 minus the sum of all squared loadings to analyse the remaining variance, e.g. if not all (robust) EMs are included (cf. Dietze et al., 2012). Negative values are set to zero.

Usage

residual.EM(Vqn)

Arguments

Vqn

Numeric matrix with m robust end-member loadings.

Value

Numeric vector with residual end-member loading.

References

Dietze E, Hartmann K, Diekmann B, IJmker J, Lehmkuhl F, Opitz S, Stauch G, Wuennemann B, Borchers A. 2012. An end-member algorithm for deciphering modern detrital processes from lake sediments of Lake Donggi Cona, NE Tibetan Plateau, China. Sedimentary Geology 243-244: 169-180.

Examples

Run this code

## Some preparing steps to retrieve only robust end-members
## load example data
data(X.artificial, envir = environment())

## truncate the data set for faster computation
X.trunc <- X.artificial[1:20,]

## define limits data set
limits = cbind(c(11, 31, 60, 78), 
               c(13, 33, 62, 80))

## define end-member numbers to test
q  <- 4:8
## define weight transformation limits to test
lw <- seq(0, 0.1, by = 0.05)
## perform the robustness test
TR  <- test.robustness(X.trunc, q, lw, c = 100)

## extract robust end-members
REM <- robust.EM(Vqsn = TR$Vqsn, limits = limits, Vqn = TR$Vqn)

## Calculation of residual end-member loading
## define mean robust end-member loadings
Vqn.rob <- REM$Vqn.mean
## perform residual end-member loading calculation
Vqn.res <- residual.EM(Vqn.rob)

# Visualisation of the result
plot(NA, xlim = c(1, 80), ylim = c(0, 1))
for(i in 1:4) {lines(Vqn.rob[i,])}
lines(Vqn.res, col = 2)