Matthews Correlation Coefficient (MCC) | A balanced binary metric

最終更新: 2025-11-03 ・ 2 分で読めます・このページを編集

まとめ

Matthews Correlation Coefficient (MCC) | A balanced binary metricの概要を押さえ、評価対象と読み取り方を整理します。
Python 3.13 のコード例で算出・可視化し、手順と実務での確認ポイントを確認します。
図表や補助指標を組み合わせ、モデル比較や閾値調整に活かすヒントをまとめます。

1. Definition #

For binary classification: \mathrm{MCC} = \frac{TP \cdot TN - FP \cdot FN}{\sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}}.

1 → perfect prediction
0 → no better than random
−1 → total disagreement Multiclass MCC generalises this formula using the complete confusion matrix.

2. Computing MCC in Python 3.13 #

python --version        # e.g. Python 3.13.0
pip install scikit-learn matplotlib

from sklearn.datasets import make_classification
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import matthews_corrcoef, confusion_matrix
from sklearn.model_selection import train_test_split
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
X, y = make_classification(
    n_samples=40_000,
    n_features=20,
    n_informative=6,
    weights=[0.95, 0.05],
    random_state=42,
)
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.25, stratify=y, random_state=42
)
model = make_pipeline(
    StandardScaler(),
    LogisticRegression(max_iter=2000, class_weight="balanced"),
)
model.fit(X_train, y_train)
y_pred = model.predict(X_test)
print(confusion_matrix(y_test, y_pred))
print("MCC:", matthews_corrcoef(y_test, y_pred))

class_weight=“balanced” helps the minority class contribute to the coefficient.

3. Threshold analysis #

MCC vs threshold — Find the threshold where MCC peaks to strike the best balance between all confusion-matrix cells.

Unlike F1, MCC rewards correct negatives as well. Evaluating it over thresholds reveals the operating point with the highest correlation.

4. Practical use cases #

Sanity-check Accuracy – a high Accuracy but low MCC signals that one class is being ignored.
Model selection – use make_scorer(matthews_corrcoef) in GridSearchCV to optimise directly for MCC.
Combine with ROC/PR curves – MCC highlights overall balance while ROC-AUC or PR curves focus on ranking/recall trade-offs.

Summary #

MCC delivers a single, balanced view of classification performance from −1 to 1.
In Python 3.13, compute it with matthews_corrcoef and visualise how it changes with the threshold.
Report MCC alongside Accuracy, F1, and PR metrics to avoid misleading conclusions on imbalanced datasets.