mlr3 (version 0.23.0)

mlr_measures_classif.mcc: Matthews Correlation Coefficient

Description

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

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

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 is 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 $s^2-\sum _k^K{p}_k^2$ or $s^2-\sum _k^K{t}_k^2)$ 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.

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.mauc_mu, 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.mauc_mu, mlr_measures_classif.mbrier