Confusion Matrix

The confusion matrix is the foundation every classification metric in this category is built from — a simple table breaking down exactly which predictions were correct, and which specific kind of mistake was made when they weren't.

The 2×2 Table (Binary Classification)

Worked Example

A spam classifier evaluated on 100 emails (30 actually spam, 70 actually not spam): it correctly flags 24 of the 30 spam emails (TP=24, so FN=6), and incorrectly flags 7 legitimate emails as spam (FP=7, so TN=63).

Every classification metric covered in the rest of this category — accuracy, precision, recall, F1, specificity — is computed directly from these four numbers.

Code

from sklearn.metrics import confusion_matrix
import numpy as np

y_true = np.array([1,1,1,1,1,0,0,0,0,0])   # 1 = spam, 0 = not spam (simplified small example)
y_pred = np.array([1,1,1,0,0,0,0,1,0,0])

cm = confusion_matrix(y_true, y_pred)
print(cm)
# [[TN FP]
#  [FN TP]]  -- note sklearn's default row/column order; always verify against your own label convention

Extending to Multi-Class

For \(K\) classes, the confusion matrix becomes a \(K\times K\) grid — row \(i\), column \(j\) counts how many examples with true class \(i\) were predicted as class \(j\). The diagonal holds every correct prediction; every off-diagonal cell represents a specific kind of confusion between two particular classes, often revealing which classes a model most often mixes up.

Common Mistakes

• Confusing which axis represents "actual" versus "predicted" — different libraries and textbooks sometimes use different row/column conventions; always check a specific tool's documentation rather than assuming.
• Stopping at just looking at the raw counts without computing any derived metric — the confusion matrix is a starting point; the next several notes turn it into single, comparable numbers.

Interview Relevance

Q: "What's the difference between a false positive and a false negative, using a medical diagnosis example?" A false positive is predicting a disease is present when it actually isn't (a healthy patient incorrectly flagged as sick) — a "false alarm." A false negative is predicting a disease is absent when it's actually present (a sick patient incorrectly cleared as healthy) — a "miss." Which error type is more costly is entirely context-dependent, and this exact distinction is why single metrics like accuracy alone are often insufficient.

Practice Question

Out of 200 patients, a diagnostic model correctly identifies 45 out of 50 actually-sick patients, and incorrectly flags 15 out of 150 actually-healthy patients as sick. Fill in the full 2×2 confusion matrix.

Related DL Notes

• Accuracy
• Precision & Recall
• Bayes' Theorem