Confusion Matrix

Eval

Confusion Matrix | Interpreting Classification Performance

Created: Last updated: Read time: 2 min
まとめ
  • Confusion Matrix | Interpreting Classification Performance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. Anatomy of a confusion matrix #

For binary classification the matrix is a 2×2 table:

Predicted: NegativePredicted: Positive
Actual: NegativeTrue Negative (TN)False Positive (FP)
Actual: PositiveFalse Negative (FN)True Positive (TP)
  • Rows represent the ground truth, columns the model prediction.
  • Inspecting TP / FP / FN / TN reveals whether the model is biased toward a specific class.

2. End-to-end example on Python 3.13 #

Make sure you are running Python 3.13 and install the required libraries:


python --version  # e.g. Python 3.13.0

pip install scikit-learn matplotlib

The script below trains a logistic regression model on the breast cancer dataset, then prints and plots the confusion matrix. A Pipeline with StandardScaler keeps the optimisation stable and avoids convergence warnings.

from pathlib import Path

import matplotlib.pyplot as plt

from sklearn.datasets import load_breast_cancer

from sklearn.linear_model import LogisticRegression

from sklearn.metrics import ConfusionMatrixDisplay, confusion_matrix

from sklearn.model_selection import train_test_split

from sklearn.pipeline import make_pipeline

from sklearn.preprocessing import StandardScaler

X, y = load_breast_cancer(return_X_y=True)

X_train, X_test, y_train, y_test = train_test_split(

    X, y, test_size=0.2, random_state=42, stratify=y

)

pipeline = make_pipeline(

    StandardScaler(),

    LogisticRegression(max_iter=1000, solver="lbfgs"),

)

pipeline.fit(X_train, y_train)

y_pred = pipeline.predict(X_test)

cm = confusion_matrix(y_test, y_pred)

print(cm)

disp = ConfusionMatrixDisplay(confusion_matrix=cm)

disp.plot(cmap="Blues", colorbar=False)

plt.tight_layout()

plt.show()
Confusion matrix for the breast cancer dataset

Confusion matrix rendered with scikit-learn (Python 3.13)

3. Normalising the matrix #

When the dataset is imbalanced, normalising by row (actual labels) helps you compare error rates.

cm_norm = confusion_matrix(y_test, y_pred, normalize="true")
print(cm_norm)
disp_norm = ConfusionMatrixDisplay(confusion_matrix=cm_norm)
disp_norm.plot(cmap="Blues", values_format=".2f", colorbar=False)
plt.tight_layout()
plt.show()
  • normalize="true": ratio within each actual class
  • normalize="pred": ratio within each predicted class
  • normalize="all": ratio over all observations

4. Extending to multiclass problems #

ConfusionMatrixDisplay.from_predictions automatically builds the matrix for multiclass tasks and adds axis labels.

ConfusionMatrixDisplay.from_predictions(

    y_true=ground_truth_labels,

    y_pred=model_outputs,

    normalize="true",

    values_format=".2f",

    cmap="Blues",

)

plt.tight_layout()

plt.show()

5. Practical checkpoints #

  • False negatives vs. false positives: decide which error is more costly (e.g., medical diagnosis vs. fraud detection) and monitor the relevant cells closely.
  • Pair with heatmaps: visual inspection highlights skewed classes and makes cross-team discussions easier.
  • Derive other metrics: accuracy, precision, recall, and F1 can all be computed from the same matrix. Compare them with ROC-AUC or PR curves for a fuller picture.
  • Keep notebooks reproducible: packaging the analysis in a Python 3.13 notebook enables fast iteration when you tune or retrain the model.

Summary #

  • A confusion matrix summarises TP / FP / FN / TN and exposes the bias of a classifier.

  • Normalising the matrix reveals error ratios when classes are imbalanced.

  • Combine the matrix with derived metrics and business requirements to define actionable evaluation criteria.