KendallCurves: Plotting Kendall Curves
In paumoal/costcurvespkg: Display and analyze Cost Curves and treshold choice

Description Usage Arguments Details Value Author(s) References See Also Examples

Function to plot the expected loss of the model, using the rate driven threshold choice method discounting the loss of a perfect ranker

KendallCurves(predictions,classes,uniquec=FALSE, loss2skew=FALSE, hold=FALSE,
               plotOFF=FALSE, gridOFF=TRUE, pointsOFF=TRUE, legendOFF=FALSE,
               main, xlab, ylab, namesClassifiers, lwd, lty, col, pch, cex,
               xPosLegend,yPosLegend, cexL)

`predictions`	A list with predicted scores.
`classes`	A list with labels, (only binary classes).
`uniquec`	If it is TRUE, the same array classes is used for each array in a list predictions.
`loss2skew`	If it is TRUE, loss by Skew is plotted otherwise loss by cost is plotted.
`hold`	If it is TRUE, the plot is maintained open allowing to insert new curves on the same plot..
`plotOFF`	Disable/enable plot visualization, only return AUC values.
`gridOFF`	Disable/enable grid visualization.
`pointsOFF`	Disable/enable point marks visualization.
`legendOFF`	Disable/enable legend visualization.
`main`	title.
`xlab`	x label.
`ylab`	y label.
`namesClassifiers`	An array with names of each classifier.
`lwd`	Line width.
`lty`	Line type.
`col`	Line color.
`pch`	Point type.
`cex`	Size point.
`xPosLegend`	x coordinate to be used to position the legend.
`yPosLegend`	y coordinate to be used to position the legend.
`cexL`	size of box legend.

The Kendall curve is defined as fallows:

Q(c)=2pi1*F1(R^-1(c)), if c<=pi0

Q(c)=2pi0(1-F0(R^-1(c))), if c>=pi0

and

R(t)=pi0*F0(t)+pi1*F1(t), by c

R(t)=(F0(t)+F1(t))/2, by z

Where:

	c:	cost values of x_axis between [0, 1].
	z:	skew values of x_axis between [0, 1].
	t:	threshold t=R^-1(c) or t=R^-1(c) as appropriate, and c=R(t)
	pi0:	negative class proportion (Y==0)/length(Y).
	pi1:	positive class proportion (Y==1)/length(Y).
	F1(t):	false positive rate of specific threshold.
	1-F0(t):	true positive rate of specific threshold.
	R(c):	recall that the predicted positive rate.

It shows for each cost proportion c, the expected loss of the model, once the loss of a perfect ranker is discounted.

An array with AUKC (Area Under Kendall Curve) for each test.

Paulina Morillo: paumoal@inf.upv.es

Hernandez-Orallo, J., Flach, P., & Ferri, C. (2013). ROC curves in cost space. Machine learning, 93(1), 71-91.

BrierCurves, CostCurves, CostLines,predictions, RateDrivenCurves, TestOptimal, TP_FP.rates, TrainOptimal

#Load data
data(predictions)

#Loss by cost
R<-KendallCurves(list(predictions$A, predictions$B), list(predictions$classes), uniquec=TRUE, 
	main="Kendall Curves")

#Loss by skew
R<-KendallCurves(list(predictions$A, predictions$B), list(predictions$classes), uniquec=TRUE,
	loss2skew = TRUE, pointsOFF=FALSE)