# Vorob: Vorob'ev computations In eaf: Plots of the Empirical Attainment Function

## Description

Compute Vorob'ev threshold, expectation and deviation. Also, displaying the symmetric deviation function is possible. The symmetric deviation function is the probability for a given target in the objective space to belong to the symmetric difference between the Vorob'ev expectation and a realization of the (random) attained set.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```vorobT(x, reference) vorobDev(x, VE, reference) symDifPlot( x, VE, threshold, nlevels = 11, ve.col = "blue", xlim = NULL, ylim = NULL, legend.pos = "topright", main = "Symmetric deviation function", col.fun = function(n) gray(seq(0, 0.9, length.out = n)^2) ) ```

## Arguments

 `x` Either a matrix of data values, or a data frame, or a list of data frames of exactly three columns. The third column gives the set (run, sample, ...) identifier. `reference` (`numeric()`) Reference point as a vector of numerical values. `VE, threshold` Vorob'ev expectation and threshold, e.g., as returned by `vorobT()`. `nlevels` number of levels in which is divided the range of the symmetric deviation. `ve.col` plotting parameters for the Vorob'ev expectation. `xlim, ylim, main` Graphical parameters, see `plot.default()`. `legend.pos` the position of the legend, see `legend()`. A value of `"none"` hides the legend. `col.fun` function that creates a vector of `n` colors, see `heat.colors()`.

## Value

`vorobT` returns a list with elements `threshold`, `VE`, and `avg_hyp` (average hypervolume)

`vorobDev` returns the Vorob'ev deviation.

Mickael Binois

## References

\insertRef

BinGinRou2015gaupareaf

C. Chevalier (2013), Fast uncertainty reduction strategies relying on Gaussian process models, University of Bern, PhD thesis.

I. Molchanov (2005), Theory of random sets, Springer.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```data(CPFs) res <- vorobT(CPFs, reference = c(2, 200)) print(res\$threshold) ## Display Vorob'ev expectation and attainment function # First style eafplot(CPFs[,1:2], sets = CPFs[,3], percentiles = c(0, 25, 50, 75, 100, res\$threshold), main = substitute(paste("Empirical attainment function, ",beta,"* = ", a, "%"), list(a = formatC(res\$threshold, digits = 2, format = "f")))) # Second style eafplot(CPFs[,1:2], sets = CPFs[,3], percentiles = c(0, 20, 40, 60, 80, 100), col = gray(seq(0.8, 0.1, length.out = 6)^0.5), type = "area", legend.pos = "bottomleft", extra.points = res\$VE, extra.col = "cyan", extra.legend = "VE", extra.lty = "solid", extra.pch = NA, extra.lwd = 2, main = substitute(paste("Empirical attainment function, ",beta,"* = ", a, "%"), list(a = formatC(res\$threshold, digits = 2, format = "f")))) # Now print Vorob'ev deviation VD <- vorobDev(CPFs, res\$VE, reference = c(2, 200)) print(VD) # Now display the symmetric deviation function. symDifPlot(CPFs, res\$VE, res\$threshold, nlevels = 11) # Levels are adjusted automatically if too large. symDifPlot(CPFs, res\$VE, res\$threshold, nlevels = 200, legend.pos = "none") # Use a different palette. symDifPlot(CPFs, res\$VE, res\$threshold, nlevels = 11, col.fun = heat.colors) ```

eaf documentation built on May 7, 2021, 5:06 p.m.