Measure to compare true observed labels with predicted probabilities in multiclass classification tasks.

## Usage

```
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.

## Details

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.

## 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.