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Матрица ошибок: объяснение

Вы построите матрицу ошибок на основе прогнозов и истинных значений, а затем выведете числа истинно положительных, ложно отрицательных и других связанных случаев

«Матрица ошибок: объяснение» — бесплатный урок Machine Learning Academy на CoddyKit. Это урок 3 из 4. Ты можешь прочитать весь урок бесплатно ниже — а потом практиковать его прямо в браузере с встроенным редактором кода и ИИ-репетитором 24/7. Это часть пути обучения Machine Learning Academy, и твой прогресс синхронизируется между веб-версией и приложением CoddyKit. Курс Machine Learning Academy содержит 4 уроков всего.

Части этого урока еще не переведены и отображаются на английском.

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.

Часто задаваемые вопросы

Урок «Матрица ошибок: объяснение» бесплатный?

Да — полный текст урока «Матрица ошибок: объяснение» бесплатно доступен здесь в веб-версии. Чтобы практиковать его интерактивно (встроенный редактор кода и ИИ-репетитор 24/7) и разблокировать остальной курс Machine Learning Academy, подпишись на CoddyKit PRO. Курс Machine Learning Academy содержит 4 уроков всего.

Чему я научусь в уроке «Матрица ошибок: объяснение»?

Вы построите матрицу ошибок на основе прогнозов и истинных значений, а затем выведете числа истинно положительных, ложно отрицательных и других связанных случаев Ты практикуешь Machine Learning Academy с помощью реального кода, который запускаешь прямо в браузере, и ИИ-репетитор 24/7 отвечает на твои вопросы во время урока.

Нужен ли мне опыт, чтобы начать Machine Learning Academy?

Предыдущий опыт не требуется. Machine Learning Academy на CoddyKit структурирован для всех уровней — от новичков до продвинутых, поэтому ты можешь начать отсюда или с самого начала и учиться в своем темпе. Это урок 3 из 4.

Сколько времени занимает урок «Матрица ошибок: объяснение»?

Большинство уроков CoddyKit занимают около 5–10 минут. Каждый из них компактный и интерактивный, поэтому ты постоянно делаешь прогресс и продолжаешь с того же места в веб-версии и приложении.

Можно ли писать и запускать код в этом уроке Machine Learning Academy?

Да. Каждый урок Machine Learning Academy включает встроенный редактор кода, поэтому ты пишешь и запускаешь реальный код прямо в браузере и получаешь моментальную обратную связь от AI — локальная установка не требуется.

Все уроки этого курса

  1. От регрессии к классификации: решения по порогу
  2. Логистическая регрессия и сигмоидальная функция
  3. Матрица ошибок: объяснение
  4. Точность, полнота и F1-мера на практике
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