plot.det: Make a Detection Error Trade-off plot
In davidavdav/sretools.R: Compute error metrics and make DET plots for NIST-like Speaker Recognition Evaluations

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

This function makes DET plot using a data structure of class det. A DET plot is a form of Receiver Operating Characteristic, but with axes warped by the quantile function of the normal distribution. DET plots are standard in Speaker Recognition detection analysis, but have application in other detection problems.

1	plot.det(x, nr = 1, lty = 1, col = nr, optimize = T, xmin = 0.1, xmax = 50, ymin = 0.1, ymax = 50, xlab = "false alarm probability (%)", ylab = "miss probability (%)", ...)

`x`	a data structure of class `det`. This can be obtained by the function `det.sre`.
`nr`	The number of the line in the DET plot. `nr=1` initiates a new plot, calls with `nr>1` cause the DET curve to be added to an existing plot.
`lty`	Line type for this plot
`col`	Color for this plot
`optimize`	Remove points in the curve that do not change the direction of the line for efficiency.
`xmin`	Minimum of the False Alarm rate, in percent
`xmax`	Maximum of the False Alarm rate, in percent
`ymin`	Minimum of the Miss rate, in percent
`ymax`	Maximum of the Miss rate, in percent
`xlab`	Label for the x-axis
`ylab`	Label for the y-axis
`...`	Additional arguments for `plot.default`

A DET plot is a standard way of showing the discrimination performance of a two-class classifier. In default axes range (0.1–50\,%) it caters for a wide range in detection performance. The axes are warped by the quantile function of the normal distribution, a.k.a. the probit function. If the scores of target an non-target trials are distributed normally, this leads to a straight line in a DET plot. (The reverse, however, does not hold).

The information in a DET plot needs to be prepared by the function det.sre, which takes a trial list and sorts scores and integrates the error rares, and determines various other performance measures.

The DET plot contains two special points, the so-called 'actual decision costs' and the ‘minimum decision costs’. The former depends on the decisions taken for each trial, and the cost function (see setDCF. It is indicated by a rectangle, where the width of the rectangle indicates the 95\,% confidence interval for the decision point. The minimum decision costs is a the operating point on the curve that indicates the minimum costs that could have been obtained using this DET and the cost function. It is indicated by a circle.

A special value of x=NULL causes an empty DET frame to be plotted, with just a grid and labeled axes.

Multiple DET curves can be made in the same plot by setting either nr>1 or lty>1.

DET plots are traditionally plotted with False Alarms (or False Positives) along the X-axis and Misses (of False Negatives) along the y-axis. Although it is possible to change the range of the axes this is discouraged; the general position of the curve within the plot gives the experienced DET plot reader an immediate feeling for the discriminability of the detector.

In psychology the measurement of miss and false alarm rates can be converted to a quantity d' (d-prime), which in a DET plot can be found by moving from the measure miss and false alarm rate point in the graph along a line of angle -45^\circ until the diagonal is crossed. The values of d' vary from 0 in the upper-right to about 6 in the lowerl left of the graph.

The function returns a list containing the important DET statistics

`Cllr`	Cost of LLR
`Cllr.min`	Minimum Cllr, computed using (weighted) isotonic regression
`EER`	The equal Error Rate, computed using the Convex Hull method
`Cdet`	The detection error costs, given the decisions in the trials
`Cdet.min`	The minimum dectection costs.
`mt`	The mean value of target scores
`mn`	The mean value of non-target scores
`nt`	The number of target trials
`nn`	The number of non-target trials
`n`	The number of trials

David A. van Leeuwen

Alvin Martin et al, “The DET Curve in Assessment of Detection Task Performance,” Proc. Interspeech, 1895–1898 (1997).

det.sre for generating a det object, setDCF for specifying the cost function, palette for controlling the colors of the curves.

## Load example SRE data:
## RU submission to EVALITA speaker recognition applications track
data(ru.2009)
setDCF("evalita")
x <- subset(ru.2009, mcond=="TC6" & tcond=="TS2")
plot(det(x), main="RU TC6 TS1 primary submission EVALITA 2009")