What is Confusion Matrix?
Confusion Matrix is a performance evaluation tool for classification models. It provides a summary of prediction results, showing how well the model predicts each class and where it makes errors. This is especially useful for binary or multi-class classification problems.
Structure of a Confusion Matrix
For binary classification, the confusion matrix is a 2×2 table:
| Predicted: Positive | Predicted: Negative | |
|---|---|---|
| Actual: Positive | True Positive (TP) | False Negative (FN) |
| Actual: Negative | False Positive (FP) | True Negative (TN) |
Explaining the Terms
1. True Positive (TP)
Definition: The model correctly identifies a positive case.
Example: A test for a disease correctly identifies a sick patient as positive.
Significance: Indicates successful prediction for the positive class.
2. True Negative (TN)
Definition: The model correctly identifies a negative case.
Example: A test correctly identifies a healthy patient as negative.
Significance: Reflects accurate prediction for the negative class.
3. False Positive (FP)
Definition: The model incorrectly identifies a negative case as positive.
Example: A test incorrectly identifies a healthy patient as sick.
Significance: Represents “false alarms,” which can lead to unnecessary actions.
4. False Negative (FN)
Definition: The model incorrectly identifies a positive case as negative.
Example: A test fails to detect a disease in a sick patient.
Significance: Indicates “missed detections,” which can have serious consequences in critical applications.
Example of a Confusion Matrix
Imagine a model designed to detect spam emails. Here’s the confusion matrix based on 100 emails:
| Predicted: Spam | Predicted: Not Spam | |
|---|---|---|
| Actual: Spam | 40 (TP) | 10 (FN) |
| Actual: Not Spam | 5 (FP) | 45 (TN) |
Metrics Derived from a Confusion Matrix
Using the values in the confusion matrix, we can calculate important metrics:
1. Accuracy
Measures the overall correctness of the model.Accuracy = (TP + TN) / (TP + TN + FP + FN)
Example:Accuracy = (40 + 45) / (40 + 45 + 5 + 10) = 0.85 (85%)
2. Precision
Focuses on how many predicted positives were correct.Precision = TP / (TP + FP)
Example:Precision = 40 / (40 + 5) = 0.89 (89%)
3. Recall (Sensitivity)
Measures how many actual positives were correctly identified.Recall = TP / (TP + FN)
Example:Recall = 40 / (40 + 10) = 0.80 (80%)
4. F1-Score
Balances precision and recall using their harmonic mean.F1-Score = 2 * (Precision * Recall) / (Precision + Recall)
Example:F1-Score = 2 * (0.89 * 0.80) / (0.89 + 0.80) ≈ 0.84 (84%)
Why is a Confusion Matrix Important?
A confusion matrix provides a detailed view of model performance, highlighting not just overall accuracy but also the types of errors the model makes. This allows practitioners to:
- Understand the trade-offs between precision and recall.
- Identify issues like class imbalance or bias.
- Optimize the model to reduce specific errors (e.g., false positives or false negatives).