Multiclass AUC measures.

*AUNU*: AUC of each class against the rest, using the uniform class
distribution. Computes the AUC treating a `c`

-dimensional classifier
as `c`

two-dimensional 1-vs-rest classifiers, where classes are assumed to have
uniform distribution, in order to have a measure which is independent
of class distribution change (Fawcett 2001).

*AUNP*: AUC of each class against the rest, using the a priori class
distribution. Computes the AUC treating a `c`

-dimensional classifier as `c`

two-dimensional 1-vs-rest classifiers, taking into account the prior probability of
each class (Fawcett 2001).

*AU1U*: AUC of each class against each other, using the uniform class
distribution. Computes something like the AUC of `c(c - 1)`

binary classifiers
(all possible pairwise combinations). See Hand (2001) for details.

*AU1P*: AUC of each class against each other, using the a priori class
distribution. Computes something like AUC of `c(c - 1)`

binary classifiers
while considering the a priori distribution of the classes as suggested
in Ferri (2009). Note we deviate from the definition in
Ferri (2009) by a factor of `c`

.
The person implementing this function and writing this very
documentation right now cautions against using this measure because it is
an imperfect generalization of AU1U.

mauc_aunu(truth, prob, na_value = NaN, ...)
mauc_aunp(truth, prob, na_value = NaN, ...)
mauc_au1u(truth, prob, na_value = NaN, ...)
mauc_au1p(truth, prob, na_value = NaN, ...)

## Arguments

truth |
:: `factor()`
True (observed) labels.
Must have the same levels and length as `response` . |

prob |
:: `matrix()`
Matrix of predicted probabilities, each column is a vector of probabilities for a
specific class label.
Columns must be named with levels of `truth` . |

na_value |
:: `numeric(1)`
Value that should be returned if the measure is not defined for the input
(as described in the note). Default is `NaN` . |

... |
:: `any`
Additional arguments. Currently ignored. |

## Value

Performance value as `numeric(1)`

.

## References

Fawcett, Tom (2001).
“Using rule sets to maximize ROC performance.”
In *Proceedings 2001 IEEE international conference on data mining*, 131--138.
IEEE.
Ferri, César, Hernández-Orallo, José, Modroiu, R (2009).
“An experimental comparison of performance measures for classification.”
*Pattern Recognition Letters*, **30**(1), 27--38.
doi: 10.1016/j.patrec.2008.08.010
.
Hand, J D, Till, J R (2001).
“A simple generalisation of the area under the ROC curve for multiple class classification problems.”
*Machine learning*, **45**(2), 171--186.

## See also

## Examples

#> [1] 0.4047619