What is a confusion matrix?
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A confusion matrix is a table used to evaluate the performance of a classification model (especially in supervised machine learning). It shows how many predictions were correct and incorrect, broken down by each class.
🔹 Structure of a Confusion Matrix (for binary classification)
| Predicted Positive | Predicted Negative | |
|---|---|---|
| Actual Positive | True Positive (TP) | False Negative (FN) |
| Actual Negative | False Positive (FP) | True Negative (TN) |
🔹 Terms Explained
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True Positive (TP): Model correctly predicts positive (e.g., correctly detecting fraud).
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True Negative (TN): Model correctly predicts negative (e.g., correctly detecting non-fraud).
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False Positive (FP): Model incorrectly predicts positive (Type I Error).
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False Negative (FN): Model incorrectly predicts negative (Type II Error).
🔹 Example
Suppose we build a spam classifier:
-
Actual spam emails: 100
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Actual non-spam emails: 100
The confusion matrix might look like:
| Predicted Spam | Predicted Not Spam | |
|---|---|---|
| Spam (100) | 90 (TP) | 10 (FN) |
| Not Spam (100) | 20 (FP) | 80 (TN) |
🔹 Metrics Derived from Confusion Matrix
From it, we can calculate:
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Accuracy = (TP + TN) / Total
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Precision = TP / (TP + FP)
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Recall (Sensitivity) = TP / (TP + FN)
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F1 Score = 2 × (Precision × Recall) / (Precision + Recall)
✅ In short: A confusion matrix tells us not just how many predictions were right or wrong, but what kind of mistakes the model made (false positives vs false negatives).
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