mlr_measures_classif.mcc {mlr3}

Matthews Correlation Coefficient

Description

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

Details

In the binary case, the Matthews Correlation Coefficient is defined as

\frac{\mathrm{TP} \cdot \mathrm{TN} - \mathrm{FP} \cdot \mathrm{FN}}{\sqrt{(\mathrm{TP} + \mathrm{FP}) (\mathrm{TP} + \mathrm{FN}) (\mathrm{TN} + \mathrm{FP}) (\mathrm{TN} + \mathrm{FN})}},

where TP, FP, TN, TP are the number of true positives, false positives, true negatives, and false negatives respectively.

In the multi-class case, the Matthews Correlation Coefficient defined for a multi-class confusion matrix C with K classes:

\frac{c \cdot s - \sum_k^K p_k \cdot t_k}{\sqrt{(s^2 - \sum_k^K p_k^2) \cdot (s^2 - \sum_k^K t_k^2)}},

where

• s = \sum_i^K \sum_j^K C_{ij}: total number of samples

• c = \sum_k^K C_{kk}: total number of correctly predicted samples

• t_k = \sum_i^K C_{ik}: number of predictions for each class k

• p_k = \sum_j^K C_{kj}: number of true occurrences for each class k.

The above formula is undefined if any of the four sums in the denominator is 0 in the binary case and more generally if either s^2 - sum(pk^2) or s^2 - sum(tk^2) is equal to 0. The denominator is then set to 1. When there are more than two classes, the MCC will no longer range between -1 and +1. Instead, the minimum value will be between -1 and 0 depending on the true distribution. The maximum value is always +1.

Dictionary

This Measure can be instantiated via the dictionary mlr_measures or with the associated sugar function msr():

mlr_measures$get("classif.mcc")
msr("classif.mcc")

Parameters

Empty ParamSet

Meta Information

• Type: "classif"

• Range: [-1, 1]

• Minimize: FALSE

• Required prediction: response

Note

The score function calls mlr3measures::mcc() from package mlr3measures.

If the measure is undefined for the input, NaN is returned. This can be customized by setting the field na_value.

See Also

Dictionary of Measures: mlr_measures

as.data.table(mlr_measures) for a complete table of all (also dynamically created) Measure implementations.

Other classification measures: mlr_measures_classif.acc, mlr_measures_classif.auc, mlr_measures_classif.bacc, mlr_measures_classif.bbrier, mlr_measures_classif.ce, mlr_measures_classif.costs, mlr_measures_classif.dor, mlr_measures_classif.fbeta, mlr_measures_classif.fdr, mlr_measures_classif.fn, mlr_measures_classif.fnr, mlr_measures_classif.fomr, mlr_measures_classif.fp, mlr_measures_classif.fpr, mlr_measures_classif.logloss, mlr_measures_classif.mauc_au1p, mlr_measures_classif.mauc_au1u, mlr_measures_classif.mauc_aunp, mlr_measures_classif.mauc_aunu, mlr_measures_classif.mbrier, mlr_measures_classif.npv, mlr_measures_classif.ppv, mlr_measures_classif.prauc, mlr_measures_classif.precision, mlr_measures_classif.recall, mlr_measures_classif.sensitivity, mlr_measures_classif.specificity, mlr_measures_classif.tn, mlr_measures_classif.tnr, mlr_measures_classif.tp, mlr_measures_classif.tpr

Other multiclass classification measures: mlr_measures_classif.acc, mlr_measures_classif.bacc, mlr_measures_classif.ce, mlr_measures_classif.costs, mlr_measures_classif.logloss, mlr_measures_classif.mauc_au1p, mlr_measures_classif.mauc_au1u, mlr_measures_classif.mauc_aunp, mlr_measures_classif.mauc_aunu, mlr_measures_classif.mbrier