混淆矩阵详解
您将根据预测结果和真实标签构建混淆矩阵，然后推导真正例、假负例及相关计数
混淆矩阵详解 是 CoddyKit 上的免费 Machine Learning Academy 课时。 这是第 3 节课，共 4 节。 你可以在下方免费阅读本课时的完整内容 — 然后在浏览器中使用内置代码编辑器和全天候 AI 导师进行实践。 这是 Machine Learning Academy 学习路径的一部分，你的进度在网页和 CoddyKit 应用中同步。 Machine Learning Academy 课程共包含 4 节课。
本课时的部分内容尚未翻译，以英文显示。
Beyond Accuracy: Understanding Errors
Accuracy tells you the percentage of correct predictions, but it treats all errors as equal. In reality, different types of errors have very different consequences. A spam filter that sends a legitimate email to the spam folder is annoying; a medical diagnosis model that misses a cancer case is life-threatening.
The confusion matrix is the tool that breaks down classifier performance into a 2×2 table (for binary classification) showing every possible combination of actual and predicted labels. It reveals not just how much the model is wrong but how it is wrong.
The Four Cells of the Confusion Matrix
For binary classification with classes Positive (1) and Negative (0), the confusion matrix has four cells:
- True Positive (TP) — actual positive, predicted positive. Correct detection.
- True Negative (TN) — actual negative, predicted negative. Correct rejection.
- False Positive (FP) — actual negative, predicted positive. Type I error; false alarm.
- False Negative (FN) — actual positive, predicted negative. Type II error; missed detection.
All four counts are needed to fully characterise a classifier's behaviour.
import numpy as np
# Medical test example:
# Positive = disease present, Negative = disease absent
y_true = np.array([1, 0, 1, 1, 0, 0, 1, 0, 1, 0])
y_pred = np.array([1, 0, 1, 0, 1, 0, 1, 0, 0, 0])
TP = ((y_pred == 1) & (y_true == 1)).sum()
TN = ((y_pred == 0) & (y_true == 0)).sum()
FP = ((y_pred == 1) & (y_true == 0)).sum()
FN = ((y_pred == 0) & (y_true == 1)).sum()
print(f'TP={TP} FP={FP}')
print(f'FN={FN} TN={TN}')
print(f'Total: {TP+TN+FP+FN}')Building the Confusion Matrix with scikit-learn
Scikit-learn's confusion_matrix() function takes the actual labels and predicted labels and returns the matrix as a NumPy array. The convention in scikit-learn is rows = actual class, columns = predicted class.
For binary classification with labels [0, 1], the matrix layout is:
- Row 0, Col 0 = TN (actual 0, predicted 0)
- Row 0, Col 1 = FP (actual 0, predicted 1)
- Row 1, Col 0 = FN (actual 1, predicted 0)
- Row 1, Col 1 = TP (actual 1, predicted 1)
from sklearn.metrics import confusion_matrix
from sklearn.linear_model import LogisticRegression
from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
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)
scaler = StandardScaler()
X_train_s = scaler.fit_transform(X_train)
X_test_s = scaler.transform(X_test)
model = LogisticRegression(max_iter=1000)
model.fit(X_train_s, y_train)
y_pred = model.predict(X_test_s)
cm = confusion_matrix(y_test, y_pred)
print('Confusion matrix:')
print(cm)
print('\nRows=Actual, Cols=Predicted')Visualising the Confusion Matrix as a Heatmap
A confusion matrix visualised as a heatmap makes the counts immediately readable. Large numbers on the diagonal (top-left to bottom-right) indicate correct predictions. Large off-diagonal numbers indicate errors that need investigation.
Use seaborn's heatmap() with annot=True and fmt='d' to display integer counts inside each cell. Adding target class names makes the plot self-explanatory without needing to consult a key.
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.metrics import confusion_matrix
cm = confusion_matrix(y_test, y_pred)
class_names = ['Malignant', 'Benign'] # breast cancer dataset
plt.figure(figsize=(7, 6))
sns.heatmap(
cm,
annot=True,
fmt='d',
cmap='Blues',
xticklabels=class_names,
yticklabels=class_names
)
plt.ylabel('Actual Label')
plt.xlabel('Predicted Label')
plt.title('Confusion Matrix — Breast Cancer Classifier')
plt.show()Deriving Accuracy from the Confusion Matrix
Every classification metric can be derived from the four confusion matrix cells. Accuracy is the simplest — it is the fraction of predictions that fall on the diagonal (TP + TN) out of all predictions:
Accuracy = (TP + TN) / (TP + TN + FP + FN)
All predictions are correct. All predictions = TP + TN + FP + FN. If your test set has 100 examples and you have TP=40, TN=50, FP=5, FN=5, then accuracy = 90/100 = 0.90. But the 5 FN errors (missed positives) may be far more consequential than the 5 FP errors.
from sklearn.metrics import confusion_matrix, accuracy_score
import numpy as np
y_true = np.array([1, 0, 1, 1, 0, 0, 1, 0, 1, 0])
y_pred = np.array([1, 0, 1, 0, 1, 0, 1, 0, 0, 0])
cm = confusion_matrix(y_true, y_pred)
TN, FP, FN, TP = cm.ravel() # for 2x2 matrix
# Manual accuracy
manual_acc = (TP + TN) / (TP + TN + FP + FN)
sklearn_acc = accuracy_score(y_true, y_pred)
print(f'TP={TP}, TN={TN}, FP={FP}, FN={FN}')
print(f'Manual accuracy: {manual_acc:.2f}')
print(f'sklearn accuracy: {sklearn_acc:.2f}')Type I and Type II Errors
In statistics and ML, errors have formal names that reflect their severity in different contexts:
- Type I error = False Positive. You raise the alarm when there is nothing to worry about. Example: flagging a legitimate transaction as fraud, sending someone to hospital unnecessarily.
- Type II error = False Negative. You miss a real event. Example: approving a fraudulent transaction, sending a cancer patient home as healthy.
In most real-world classification problems, Type I and Type II errors have very different costs, which is why a single accuracy number is insufficient for decision-making.
The Confusion Matrix for Multi-Class Problems
For a k-class problem, the confusion matrix is k×k. Each row represents an actual class and each column represents a predicted class. Diagonal elements are correct predictions; off-diagonal elements are misclassifications.
Multi-class confusion matrices reveal which classes the model confuses most. For example, a digit recogniser might frequently confuse 4s and 9s because they look similar. This insight guides targeted improvements: collect more training examples of confused classes, add features that distinguish them, or post-process predictions for those specific pairs.
from sklearn.metrics import confusion_matrix
from sklearn.tree import DecisionTreeClassifier
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split
import seaborn as sns
import matplotlib.pyplot as plt
X, y = load_digits(return_X_y=True)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
model = DecisionTreeClassifier(max_depth=10)
model.fit(X_train, y_train)
y_pred = model.predict(X_test)
cm = confusion_matrix(y_test, y_pred)
plt.figure(figsize=(9, 7))
sns.heatmap(cm, annot=True, fmt='d', cmap='Blues')
plt.title('Digit Confusion Matrix (10 classes)')
plt.show()Normalised Confusion Matrix
When classes have different numbers of examples (class imbalance), absolute counts in the confusion matrix can be misleading. A normalised confusion matrix divides each row by the total number of actual examples in that class, converting raw counts to recall rates (proportion correctly identified).
A perfect classifier has 1.0 on every diagonal cell and 0.0 everywhere else. A normalised matrix makes it easy to compare per-class performance regardless of class size.
from sklearn.metrics import confusion_matrix
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
cm = confusion_matrix(y_test, y_pred)
# Normalise by row (actual class total)
cm_norm = cm.astype(float) / cm.sum(axis=1, keepdims=True)
plt.figure(figsize=(9, 7))
sns.heatmap(cm_norm, annot=True, fmt='.2f', cmap='Blues')
plt.ylabel('Actual Class')
plt.xlabel('Predicted Class')
plt.title('Normalised Confusion Matrix (row = recall per class)')
plt.show()
# Per-class recall from diagonal
print('Per-class recall:', np.diag(cm_norm).round(3))ConfusionMatrixDisplay: The Official scikit-learn Tool
Scikit-learn provides ConfusionMatrixDisplay as a high-level tool for plotting confusion matrices without needing seaborn. You can create it directly from the confusion matrix array or by calling from_estimator() which runs prediction internally.
Setting display_labels to your class names makes the plot immediately self-documenting. The display also includes an optional colour bar that helps readers estimate values before reading exact numbers.
from sklearn.metrics import ConfusionMatrixDisplay
from sklearn.datasets import load_breast_cancer
X, y = load_breast_cancer(return_X_y=True)
class_names = load_breast_cancer().target_names # ['malignant', 'benign']
# Method 1: from_estimator (runs predict internally)
disp = ConfusionMatrixDisplay.from_estimator(
model,
X_test_s,
y_test,
display_labels=class_names,
cmap='Blues'
)
disp.ax_.set_title('Confusion Matrix')What the Confusion Matrix Tells You
A well-trained classifier should have most examples on the diagonal. When you see large off-diagonal numbers, diagnose the cause:
- Many FP (false positives): the model is too aggressive — lower the decision threshold or add regularisation.
- Many FN (false negatives): the model misses too many real positives — lower the threshold or improve recall.
- Symmetric errors between class A and B: the two classes are too similar in feature space — add distinguishing features.
- Errors concentrated in one actual class: that class is underrepresented or harder to learn — oversample it or collect more data.
Confusion Matrix to Full Classification Report
Every metric in the classification_report() is derived from the confusion matrix. Understanding the matrix is understanding all metrics at once. From TP, TN, FP, FN you can compute:
- Accuracy = (TP+TN)/N
- Precision = TP/(TP+FP)
- Recall = TP/(TP+FN)
- Specificity = TN/(TN+FP)
- F1 = 2×Precision×Recall/(Precision+Recall)
In the next lesson you will master all these derived metrics and learn when each one is the right choice.
from sklearn.metrics import classification_report, confusion_matrix
import numpy as np
y_true = np.array([1, 0, 1, 1, 0, 0, 1, 0, 1, 0])
y_pred = np.array([1, 0, 1, 0, 1, 0, 1, 0, 0, 0])
cm = confusion_matrix(y_true, y_pred)
TN, FP, FN, TP = cm.ravel()
# Compute all metrics from raw counts
precision = TP / (TP + FP) if (TP + FP) > 0 else 0
recall = TP / (TP + FN) if (TP + FN) > 0 else 0
f1 = 2 * precision * recall / (precision + recall) if (precision + recall) > 0 else 0
print(f'Precision: {precision:.2f}')
print(f'Recall: {recall:.2f}')
print(f'F1-Score: {f1:.2f}')
print('\nscikit-learn report:')
print(classification_report(y_true, y_pred))Quick Check
Test your understanding of Machine Learning with Python concepts from this lesson.
Lesson Recap
In this lesson you learned: the confusion matrix breaks down classifier errors into True Positives, True Negatives, False Positives, and False Negatives, False Negatives (Type II errors) and False Positives (Type I errors) have very different real-world consequences, and all classification metrics — accuracy, precision, recall, F1 — are derived from these four confusion matrix counts. Next up we master precision, recall, and F1-score in depth, and learn the critical trade-off between them that guides real-world classifier evaluation.
常见问题解答
「混淆矩阵详解」课时是免费的吗？
是的 — 「混淆矩阵详解」的完整文本可在网页上免费阅读。要进行交互式练习（内置代码编辑器和全天候 AI 导师）并解锁 Machine Learning Academy 课程的其余内容，请升级到 CoddyKit PRO。 Machine Learning Academy 课程共包含 4 节课。
「混淆矩阵详解」这节课中我会学到什么？
您将根据预测结果和真实标签构建混淆矩阵，然后推导真正例、假负例及相关计数 你通过在浏览器中直接运行的动手代码来练习 Machine Learning Academy，全天候 AI 导师会在你学习这节课的过程中回答你的问题。
学习 Machine Learning Academy 需要有经验吗？
无需任何先前经验。CoddyKit 上的 Machine Learning Academy 课程适合初学者到高级学习者，你可以从这里开始或从头开始，按照自己的节奏学习。 这是第 3 节课，共 4 节。
「混淆矩阵详解」课时需要多长时间？
大多数 CoddyKit 课程大约需要 5–10 分钟。每节课都很精短且互动，所以你能稳步进步，并在网页和应用中从离开的地方继续。
我能在这节 Machine Learning Academy 课中编写并运行代码吗？
能。每节 Machine Learning Academy 课都包含内置代码编辑器，你可以在浏览器中直接编写并运行真实代码，并获得即时 AI 反馈 — 无需本地设置。