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The Confusion Matrix

A Confusion Matrix is a table used to describe the performance of a classification model. While "Accuracy" tells you how often the model is correct, the Confusion Matrix tells you exactly how it is failing and which classes are being swapped.

1. The 2x2 Layout​

For a binary classification (Yes/No, Spam/Ham), the matrix consists of four quadrants:

Predicted: NegativePredicted: Positive
Actual: NegativeTrue Negative (TN)False Positive (FP)
Actual: PositiveFalse Negative (FN)True Positive (TP)

Breaking Down the Quadrants:​

  • True Positive (TP): You predicted positive, and it was true. (e.g., You predicted a patient has cancer, and they do).
  • True Negative (TN): You predicted negative, and it was true. (e.g., You predicted a patient is healthy, and they are).
  • False Positive (FP): You predicted positive, but it was false. (Also known as a Type I Error or a "False Alarm").
  • False Negative (FN): You predicted negative, but it was positive. (Also known as a Type II Error or a "Miss").

2. Type I vs. Type II Errors​

The "cost" of these errors depends entirely on your specific problem.

  • In Cancer Detection: A Type II Error (FN) is much worse because a sick patient goes untreated.
  • In Spam Filtering: A Type I Error (FP) is worse because an important work email is hidden in the trash.

3. Implementation with Scikit-Learn​

from sklearn.metrics import confusion_matrix, ConfusionMatrixDisplay
import matplotlib.pyplot as plt

# Actual values and Model predictions
y_true = [0, 1, 0, 1, 0, 1, 1, 0]
y_pred = [0, 1, 1, 1, 0, 0, 1, 0]

# 1. Generate the matrix
cm = confusion_matrix(y_true, y_pred)

# 2. Visualize it
disp = ConfusionMatrixDisplay(confusion_matrix=cm, display_labels=['Negative', 'Positive'])
disp.plot(cmap=plt.cm.Blues)
plt.show()

4. Multi-Class Confusion Matrices​

The matrix isn't just for binary problems. If you are classifying "Cat," "Dog," and "Bird," your matrix will be 3x3. The diagonal line from top-left to bottom-right represents correct predictions. Any numbers off that diagonal show you which animals the model is confusing.

5. Summary: What can we calculate from here?​

The Confusion Matrix is the "mother" of all classification metrics. From these four numbers, we derive:

  • Accuracy:
  • Precision:
  • Recall:
  • F1-Score: The balance between Precision and Recall.

References​

Now that you can see where the model is making mistakes, let's learn how to turn those mistakes into a single score.