mcc {mlr3measures}

Matthews Correlation Coefficient

Description

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

Usage

mcc(truth, response, positive = NULL, ...)

Arguments

truth

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

response

(factor())
Predicted response labels. Must have the same levels and length as truth.

positive

(⁠character(1⁠) Name of the positive class in case of binary classification.

...

(any)
Additional arguments. Currently ignored.

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.

Value

Performance value as numeric(1).

Meta Information

• Type: "classif"

• Range: [-1, 1]

• Minimize: FALSE

• Required prediction: response

References

https://en.wikipedia.org/wiki/Phi_coefficient

Matthews BW (1975). “Comparison of the predicted and observed secondary structure of T4 phage lysozyme.” Biochimica et Biophysica Acta (BBA) - Protein Structure, 405(2), 442–451. doi:10.1016/0005-2795(75)90109-9.

See Also

Other Classification Measures: acc(), bacc(), ce(), logloss(), mauc_aunu(), mbrier(), zero_one()

Examples

set.seed(1)
lvls = c("a", "b", "c")
truth = factor(sample(lvls, 10, replace = TRUE), levels = lvls)
response = factor(sample(lvls, 10, replace = TRUE), levels = lvls)
mcc(truth, response)